HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 04 Aug 2020 11:59:20 GMT2020-08-04T11:59:20Z50731- Some results on the mean square formula for the riemann zeta-functionhttp://hdl.handle.net/10722/32889Title: Some results on the mean square formula for the riemann zeta-function
Authors: Lau, Yuk-kam.; 劉旭金
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10722/328891993-01-01T00:00:00Z
- Error terms in the summatory formulas for certain number-theoretic functionshttp://hdl.handle.net/10722/35233Title: Error terms in the summatory formulas for certain number-theoretic functions
Authors: Lau, Yuk-kam.; 劉旭金
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/352331999-01-01T00:00:00Z
- The number of Hecke eigenvalues of same signshttp://hdl.handle.net/10722/156249Title: The number of Hecke eigenvalues of same signs
Authors: Lau, YK; Wu, J
Abstract: We give the best possible lower bounds in order of magnitude for the number of positive and negative Hecke eigenvalues. This improves upon a recent work of Kohnen, Lau and Shparlinski. Also, we study an analogous problem for short intervals. © Springer-Verlag 2008.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1562492009-01-01T00:00:00Z
- On the limiting distribution of a generalized divisor problem for the case -1/2 < a < 0http://hdl.handle.net/10722/156096Title: On the limiting distribution of a generalized divisor problem for the case -1/2 < a < 0
Authors: Lau, YK
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1560962001-01-01T00:00:00Z
- Average values of divisor sums in arithmetic progressionshttp://hdl.handle.net/10722/241850Title: Average values of divisor sums in arithmetic progressions
Authors: Lau, YK
Abstract: The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concerned with the sum $S(X,q,b)=\sum_{n \le x, n \cong b \mod q} \tau(n)$. When q=1, Drichlet derived in 1849 a pretty asymptotic formula with elementary methods. For the general case, Selberg and Hooley independently discovered the aymtotic formula $ S(X,q,b)=\frac{1}{\phi(q)}\{XP_q(\log X)+O(X^{1-\delta}\}$ for some $\de >0$ where $\phi(q)$ is the Euler phi function and $P_Q(x)$ is a linear polynomial in x. In this talk, we study the derivation of S(X,q,b) from the main term on average over b. This problem was investigated in a few papers by Banks et al. Blomer, Lu etc. We shall discuss the recent progress, applications and some ideas of proofs.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2418502011-01-01T00:00:00Z
- On modular signshttp://hdl.handle.net/10722/156262Title: On modular signs
Authors: Kowalski, E; Lau, YK; Soundararajan, K; Wu, J
Abstract: We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular form, and we give both individual and statistical results. The second problem, which has been considered by a number of authors, is to determine the size, in terms of the conductor and weight, of the first sign-change of Hecke eigenvalues. Here we improve the recent estimate of Iwaniec, Kohnen and Sengupta. © Cambridge Philosophical Society 2010.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1562622010-01-01T00:00:00Z
- Frequency of oscillations of an error term related to the Euler functionhttp://hdl.handle.net/10722/156101Title: Frequency of oscillations of an error term related to the Euler function
Authors: Lau, YK; Pétermann, YFS
Abstract: Let φ be the Euler function, and consider the error term H in the asymptotic formula Σn≤x φ(n)/n = 6/π2x+H(X). It is proved that, for any fixed real number A, there are at least CAT+ 0(1) integers n ∈[1, T] such that (H(n) - A)(H(n+1)-A)<0, where 0 < CA < 1 is a constant depending on A.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1561012000-01-01T00:00:00Z
- On the error term in an asymptotic formula for the symmetric square L-functionhttp://hdl.handle.net/10722/158859Title: On the error term in an asymptotic formula for the symmetric square L-function
Authors: Lau, YK
Abstract: Recently Wu proved that for all primes q, ∑ f L(1, sym 2 f) = π 4/432 q + O(q 27/28 log B q) where f runs over all normalized newforms of weight 2 and level q. Here we show that 27/28 can be replaced by 9/10.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1588592004-01-01T00:00:00Z
- Values of L-functions at the boundary point 1http://hdl.handle.net/10722/251905Title: Values of L-functions at the boundary point 1
Authors: Lau, YK
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2519052017-01-01T00:00:00Z
- Statistics of Hecke eigenvalueshttp://hdl.handle.net/10722/251906Title: Statistics of Hecke eigenvalues
Authors: Lau, YK
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2519062017-01-01T00:00:00Z
- Shifted convolution sums of Fourier coefficients of cusp formshttp://hdl.handle.net/10722/119239Title: Shifted convolution sums of Fourier coefficients of cusp forms
Authors: Lau, YK; Liu, J; Ye, Y
Description: Proceedings of the 4th China-Japan Seminar, Weihai, China, 30 August – 3 September 2006
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/1192392007-01-01T00:00:00Z
- On the mean square formula of the error term for a class of arithmetical functionshttp://hdl.handle.net/10722/156033Title: On the mean square formula of the error term for a class of arithmetical functions
Authors: Lau, YK
Abstract: Based on the method in MEURMAN [5], we study the mean square formula of the error term for a class of Arithmetical functions whose Dirichlet series satisfies a functional equation with multiple gamma factors. We obtain improvements on some results of CHANDRASEKHARAN and NARASIMHAN [1].
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/1560331999-01-01T00:00:00Z
- On a weighted mean square result of the error terms of some arithmetical functionshttp://hdl.handle.net/10722/156081Title: On a weighted mean square result of the error terms of some arithmetical functions
Authors: Lau, YK
Abstract: Let a(n) be an arithmetical function satisfying some conditions and write ∑′n≤xa(n)=main term+E(x). We obtain an asymptotic formula for a weighted mean square of the error term∫1T|E(y)|2y2σ 0 +1dy∼clogT for some constants σ0 and c, by modifying a method that seems due to Titchmarsh. This method utilizes the following tools: the Perron formula, the Parseval Theorem, and a Tauberian Theorem. The main difference between the present and the original method is that we include the contribution of the poles of the associated Dirichlet series on a certain line in the main term. © 2000 Academic Press.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10722/1560812000-01-01T00:00:00Z
- Equidistribution of hecke eigenforms on the arithmetic surface Γ0(N)\Hhttp://hdl.handle.net/10722/156089Title: Equidistribution of hecke eigenforms on the arithmetic surface Γ0(N)\H
Authors: Lau, YK
Abstract: Given the orthonormal basis of Hecke eigenforms in S2k(Γ(1)), Luo established an associated probability measured k on the modular surface Γ(1)\H that tends weakly to the invariant measure on Γ(1)\H. We generalize his result to the arithmetic surface Γ0(N)\H where N > 1 is square-free. © Elsevier Science (USA).
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1560892002-01-01T00:00:00Z
- Quantitative version of the joint distribution of eigenvalues of the Hecke operatorshttp://hdl.handle.net/10722/156269Title: Quantitative version of the joint distribution of eigenvalues of the Hecke operators
Authors: Lau, YK; Wang, Y
Abstract: Recently, Murty and Sinha proved an effective/quantitative version of Serre's equidistribution theorem for eigenvalues of Hecke operators on the space of primitive holomorphic cusp forms. In the context of primitive Maass forms, Sarnak figured out an analogous joint distribution. In this paper, we prove a quantitative version of Sarnak's theorem that gives explicitly estimate on the rate of convergence. The same result also holds for the case of holomorphic cusp forms. © 2011 Elsevier Inc.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1562692011-01-01T00:00:00Z
- Fourier coefficients of half-integral weight modular formshttp://hdl.handle.net/10722/240475Title: Fourier coefficients of half-integral weight modular forms
Authors: Lau, YK
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2404752016-01-01T00:00:00Z
- On the tails of the limiting distribution function of the error term in the Dirichlet divisor problemhttp://hdl.handle.net/10722/75291Title: On the tails of the limiting distribution function of the error term in the Dirichlet divisor problem
Authors: Lau, YK
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/752912001-01-01T00:00:00Z
- Sums of some multiplicative functions over a special set of integershttp://hdl.handle.net/10722/75270Title: Sums of some multiplicative functions over a special set of integers
Authors: Lau, YK; Wu, J
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/752702002-01-01T00:00:00Z
- Extreme values of symmetric power L-functions at 1http://hdl.handle.net/10722/75212Title: Extreme values of symmetric power L-functions at 1
Authors: Lau, YK; Wu, J
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/752122007-01-01T00:00:00Z
- On the least quadratic non-residuehttp://hdl.handle.net/10722/75186Title: On the least quadratic non-residue
Authors: Lau, YK; Wu, J
Abstract: We prove that for almost all real primitive characters χd of modulus d , the least positive integer nχd at which χd d takes a value not equal to 0 and 1 satisfies nχd ≪ log d , and give a quite precise estimate on the size of the exceptional set. © 2008 World Scientific Publishing Company.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/751862008-01-01T00:00:00Z
- Sign changes of the Fourier coefficients of modular formshttp://hdl.handle.net/10722/253290Title: Sign changes of the Fourier coefficients of modular forms
Authors: Lau, YK
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2532902015-01-01T00:00:00Z
- A mean square formula for central values of twisted automorphic L-functionshttp://hdl.handle.net/10722/75189Title: A mean square formula for central values of twisted automorphic L-functions
Authors: Lau, YK; Tsang, KM
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/751892005-01-01T00:00:00Z
- Coefficients of symmetric square L-functionshttp://hdl.handle.net/10722/142366Title: Coefficients of symmetric square L-functions
Authors: Lau, YK; Liu, JY; Wu, J
Abstract: Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f. We prove Ω± results for λsym2f(n) and evaluate the number of positive (resp., negative) λsym2f(n) in some intervals. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1423662010-01-01T00:00:00Z
- A vector - host epidemic modelhttp://hdl.handle.net/10722/75169Title: A vector - host epidemic model
Authors: Ching, WK; Chung, SK; Lau, YK; Ng, TW; Yung, SP
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/751692002-01-01T00:00:00Z
- A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip 3/4 ≤ σ < 1http://hdl.handle.net/10722/75172Title: A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip 3/4 ≤ σ < 1
Authors: Lau, YK
Abstract: Let $E_sigma (T)$ be the error term in the mean square formula of the Riemann zeta-function in the critical strip $1/2<sigma <1$. It is an analogue of the classical error term $E(T)$. The research of $E(T)$ has a long history but the investigation of $E_sigma (T)$ is quite new. In particular there is only a few information known about $E_sigma (T)$ for $3/4<sigma <1$. As an exploration, we study its mean value $int _1^TE_sigma (u),du$. In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of $T$.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/751722006-01-01T00:00:00Z
- Mean square of the remainder term in the Dirichlet divisor problemhttp://hdl.handle.net/10722/75300Title: Mean square of the remainder term in the Dirichlet divisor problem
Authors: Lau, YK; Tsang, KM
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10722/753001995-01-01T00:00:00Z
- Ω±-Results of the error term in the mean square formula of the Riemann zeta-function in the critical striphttp://hdl.handle.net/10722/156105Title: Ω±-Results of the error term in the mean square formula of the Riemann zeta-function in the critical strip
Authors: Lau, YK; Tsang, KM
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1561052001-01-01T00:00:00Z
- On the limiting distribution of a generalized divisor problem for the case -1 ≤ a < - 1/2http://hdl.handle.net/10722/156104Title: On the limiting distribution of a generalized divisor problem for the case -1 ≤ a < - 1/2
Authors: Lau, YK
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/1561042001-01-01T00:00:00Z
- Sign changes of error terms related to the Euler functionhttp://hdl.handle.net/10722/156095Title: Sign changes of error terms related to the Euler function
Authors: Lau, YK
Abstract: Let φ(n) be the Euler function (i.e., φ(n) denotes the number of integers less than n which are relatively prime to n), and define
R(x)= ∑n<=x φ(n)- 3/π2 x2, H(x)= ∑n<=x φ(n)/n - 6/π2 x. These functions were extensively studied by several mathematicians. One of the problems investigated concerns their sign changes. We say that a function fx) has a sign change at x = x0 if f(x0 −) f(x0 +) < 0, and f(x) has a sign change on the integer n if (n)f(n+1) < 0. The numbers of sign changes and sign changes on integers of f(x) in the interval [1, T] are denoted by Xf(T) and Nf(T), respectively.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10722/1560951999-01-01T00:00:00Z
- On the number of sign changes of hecke eigenvalues of newformshttp://hdl.handle.net/10722/58959Title: On the number of sign changes of hecke eigenvalues of newforms
Authors: Kohnen, W; Lau, YK; Shparlinski, IE
Abstract: We show that, for every x exceeding some explicit bound depending only on k and N, there are at least C(k,N)x/log17x positive and negative coefficients a(n) with n ≤ x in the Fourier expansion of any non-zero cuspidal Hecke eigenform of even integral weight k ≥ 2 and squarefree level N that is a newform, where C(k,N) depends only on k and N. From this we deduce the existence of a sign change in a short interval. © 2008 Copyright 2008 Australian Mathematical Society.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/589592008-01-01T00:00:00Z
- Omega result for the mean square of the Riemann zeta functionhttp://hdl.handle.net/10722/75179Title: Omega result for the mean square of the Riemann zeta function
Authors: Lau, YK; Tsang, KM
Abstract: A recent method of Soundararajan enables one to obtain improved Ω-result for finite series of the form Σn f(n) cos (2π λ n x+β) where 0<λ 1<λ 2<. . . and β are real numbers and the coefficients f(n) are all non-negative. In this paper, Soundararajan's method is adapted to obtain improved Ω-result for E(t), the remainder term in the mean-square formula for the Riemann zeta-function on the critical line. The Atkinson series for E(t) is of the above type, but with an oscillating factor (-1) n attached to each of its terms. © Springer-Verlag 2005.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/751792005-01-01T00:00:00Z
- An estimate for symmetric square L-functions on weight aspecthttp://hdl.handle.net/10722/75151Title: An estimate for symmetric square L-functions on weight aspect
Authors: Lau, YK
Abstract: We establish a mean square estimate on the weight aspect for symmetric square L-functions at every point on the critical line.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/751512003-01-01T00:00:00Z
- On a generalized divisor problem Ihttp://hdl.handle.net/10722/75462Title: On a generalized divisor problem I
Authors: Lau, YK
Abstract: We give a discussion on the properties of δa(x) (-1 < a < 0), which is a generalization of the error term δ(x) in the Dirichlet divisor problem. In particular, we study its oscillatory nature and investigate the gaps between its sign-changes for -1/2 ≤ a < 0.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/754622002-01-01T00:00:00Z
- On a generalized divisor problem IIhttp://hdl.handle.net/10722/75417Title: On a generalized divisor problem II
Authors: Lau, YK
Abstract: We investigate the ω±-result of Δ a(x) and its number of sign-changes in an interval [1,T], denoted by Xa(T), for -1 ≤ a < -1/2. We can prove that T ≫a Xa(T) which is the best possible in order of magnitude.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/754172003-01-01T00:00:00Z
- Moments over short intervalshttp://hdl.handle.net/10722/75301Title: Moments over short intervals
Authors: Lau, YK; Tsang, KM
Abstract: An asymptotic result for the kth moment (k ≦ 9) of the error term in the Dirichlet divisor problem over short intervals is obtained, which improves on an earlier result of Nowak. © Birkhäuser Verlag, Basel, 2005.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/753012005-01-01T00:00:00Z
- Local distribution of ordered factorizations of integershttp://hdl.handle.net/10722/75246Title: Local distribution of ordered factorizations of integers
Authors: Lau, YK
Abstract: Denote am(n) = ∑ n1, ..., nm ≥ 2 n1 ... nm = n 1 to be the number of ordered factorizations of an integer n into m factors. We are concerned with the local distribution A(x,m) = ∑n ≤ x am (n). A recent work of Hwang studied A(x, m) by using two methods: the analytic method and saddle-point method. Hwang then concluded a simple asymptotic formula for m = o((log x)2/3). We prove here that the analytic method is in fact sufficient to yield this formula, and moreover, give some refinements. © 2001 Elsevier Science.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10722/752462001-01-01T00:00:00Z
- Half-integral weight modular forms and L-functionshttp://hdl.handle.net/10722/236934Title: Half-integral weight modular forms and L-functions; 半整权模形式及L-函数
Authors: Lau, YK; Royer, E; Wu, J
Abstract: 报告的第二部分，将介绍Hecke算子，Hecke特征形， L-函数及其解析性质.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2369342016-01-01T00:00:00Z
- Quantitative analysis of the Satake parameters of GL2 representations with prescribed local representationshttp://hdl.handle.net/10722/217070Title: Quantitative analysis of the Satake parameters of GL2 representations with prescribed local representations
Authors: Lau, YK; Li, C; Wang, Y
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2170702014-01-01T00:00:00Z
- The first negative coefficients of symmetric square L-functionshttp://hdl.handle.net/10722/156284Title: The first negative coefficients of symmetric square L-functions
Authors: Lau, YK; Liu, JY; Wu, J
Abstract: Let n sym2f be the greatest integer such that b.λ sym2 f(n) ≥ 0 for all n <n sym2f and (n,N) equals 1, where b.lambda sym2f(n) is the nth coefficient of the Dirichlet series representation of the symmetric square L-function L(s,sym 2f) associated to a primitive form f of level N and of weight k. In this paper, we establish the subconvexity bound:n sym2f <(k 2N 2) 40/113 where the implied constant is absolute. © 2011 Springer Science+Business Media, LLC.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1562842012-01-01T00:00:00Z
- On the existence of limiting distributions of some number-theoretic error termshttp://hdl.handle.net/10722/75371Title: On the existence of limiting distributions of some number-theoretic error terms
Authors: Lau, YK
Abstract: We prove the existence of the limiting distribution of a class of functions which are bounded and can be approximated by periodic functions in L1-norm. This had been investigated by Heath-Brown and our work is a generalization. A tool used here is the continuity theorem. By using its quantitative version, we can investigate the rate of convergence of some cases. © 2002 Elsevier Science (USA).
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/753712002-01-01T00:00:00Z
- Fourier coefficients of half-integral weight modular formshttp://hdl.handle.net/10722/252374Title: Fourier coefficients of half-integral weight modular forms
Authors: Lau, YK
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2523742017-01-01T00:00:00Z
- Sums of fourier coefficients of CUSP formshttp://hdl.handle.net/10722/144542Title: Sums of fourier coefficients of CUSP forms
Authors: Lau, YK; Lü, G
Abstract: Let tφ(n) denote the nth normalized Fourier coefficient of a primitive holomorphic or Maass cusp form φ for the full modular group SL(2,ℤ). In this paper, we are concerned with the upper bound and omega results for the summatory function ∑n≤xt φ(nj) Asymptotic formulae for high power moments of tφ(n) are (conditionally) established. © 2010. Published by Oxford University Press. All rights reserved.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1445422011-01-01T00:00:00Z
- An omega result for supremum norms of Hecke-eigenforms in the level aspecthttp://hdl.handle.net/10722/156251Title: An omega result for supremum norms of Hecke-eigenforms in the level aspect
Authors: Lau, YK
Abstract: This note is to remark the large supremum norms of some Hecke-eigenforms of large squarefree levels and nebentypus of small conductors, based on the recent prominent progress by Soundararajan on the extreme central values of L-functions. © Science China Press and Springer-Verlag Berlin Heidelberg 2010.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1562512010-01-01T00:00:00Z
- Non-vanishing of symmetric square L-functionshttp://hdl.handle.net/10722/43002Title: Non-vanishing of symmetric square L-functions
Authors: Lau, YK
Abstract: Given a complex number s with 0 < ℛe s < 1, we study the existence of a cusp form of large even weight for the full modular group such that its associated symmetric square L-function L(sym2f, s) does not vanish. This problem is also considered in other articles.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/430022002-01-01T00:00:00Z
- Average values of Fourier coefficients of holomorphic primitive forms in arithmetic progressionshttp://hdl.handle.net/10722/242551Title: Average values of Fourier coefficients of holomorphic primitive forms in arithmetic progressions
Authors: Lau, YK
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2425512011-01-01T00:00:00Z
- On a variance of Hecke eigenvalues in arithmetic progressionshttp://hdl.handle.net/10722/156279Title: On a variance of Hecke eigenvalues in arithmetic progressions
Authors: Lau, YK; Zhao, L
Abstract: Let a(n) be the eigenvalue of a holomorphic Hecke eigenform f under the nth Hecke operator. We derive asymptotic formulae for the variance ∑ b=1 q|∑ n≤Xn≡ b(modq)a(n)| 2 when X 1/4+ε≤q≤X 1/2-ε or X 1/2+ε≤q≤X 1-ε, that exhibit distinct behavior. The analogous problem for the divisor function will be studied as well. © 2012 Elsevier Inc.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1562792012-01-01T00:00:00Z
- Omega result for the error term in the mean square formula for dirichlet L-functionshttp://hdl.handle.net/10722/75460Title: Omega result for the error term in the mean square formula for dirichlet L-functions
Authors: Lau, YK; Tsang, KM
Abstract: Let q be a positive integer and let E(q, x) denote the error term in the asymptotic formula for the mean value ∑χ mod q ∫x 0 |L(1/2 + it, χ)|2 dt. We obtain in this paper an Ω-result for E(q, x), which is an extension of the corresponding Ω-result for the Riemann zeta-function.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/754602008-01-01T00:00:00Z
- On the error term of the mean square formula for the Riemann zeta-function in the critical strip 3/4 < σ < 1http://hdl.handle.net/10722/156171Title: On the error term of the mean square formula for the Riemann zeta-function in the critical strip 3/4 < σ < 1
Authors: Lau, YK
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/1561712002-01-01T00:00:00Z
- Twisted moments of automorphic L-functionshttp://hdl.handle.net/10722/156258Title: Twisted moments of automorphic L-functions
Authors: Lau, YK; Royer, E; Wu, J
Abstract: We study the moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the square of the value of the standard L-function at the center of the critical strip. We give a precise expansion of the moments as the order goes to infinity. © 2010 Elsevier Inc.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1562582010-01-01T00:00:00Z
- Summatory formula of the convolution of two arithmetical functionshttp://hdl.handle.net/10722/75481Title: Summatory formula of the convolution of two arithmetical functions
Authors: Lau, YK
Abstract: We study the asymptotic formula of ∑n≤x f * g(n) for some arithmetical functions f and g. This generalizes the case 1 * v(n) investigated by Balakrishnan and Pétermann.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10722/754812002-01-01T00:00:00Z