Links for fulltext
(May Require Subscription)
- Publisher Website: 10.4310/MRL.2011.v18.n4.a2
- Scopus: eid_2-s2.0-80051970935
- Find via
Supplementary
-
Citations:
- Scopus: 0
- Appears in Collections:
Article: Faber polynomials and poincaré series
Title | Faber polynomials and poincaré series Faber polynomials and poincare series |
---|---|
Authors | |
Issue Date | 2011 |
Citation | Mathematical Research Letters, 2011, v. 18 n. 4, p. 591-611 How to Cite? |
Abstract | In this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z). The space has a distinguished set of generators f2−k,m. Such weakly holomorphic modular forms have been classified in terms of finitely many Eisenstein series, the unique weight 12 newform Δ, and certain Faber polynomials in the modular invariant j(z), the Hauptmodul for \SL2(\Z). We employ the theory of harmonic weak Maass forms and (non-holomorphic) Maass–Poincaré series in order to obtain the asymptotic growth of the coefficients of these Faber polynomials. Along the way, we obtain an asymptotic formula for the partial derivatives of the Maass–Poincaré series with respect to y as well as extending an asymptotic for the growth of the ℓth repeated integral of the Gauss error function at x to include ℓ∈\R and a wider range of x. |
Persistent Identifier | http://hdl.handle.net/10722/192197 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 1.128 |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kane, B | en_US |
dc.date.accessioned | 2013-10-23T09:27:18Z | - |
dc.date.available | 2013-10-23T09:27:18Z | - |
dc.date.issued | 2011 | en_US |
dc.identifier.citation | Mathematical Research Letters, 2011, v. 18 n. 4, p. 591-611 | en_US |
dc.identifier.issn | 1073-2780 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/192197 | - |
dc.description.abstract | In this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z). The space has a distinguished set of generators f2−k,m. Such weakly holomorphic modular forms have been classified in terms of finitely many Eisenstein series, the unique weight 12 newform Δ, and certain Faber polynomials in the modular invariant j(z), the Hauptmodul for \SL2(\Z). We employ the theory of harmonic weak Maass forms and (non-holomorphic) Maass–Poincaré series in order to obtain the asymptotic growth of the coefficients of these Faber polynomials. Along the way, we obtain an asymptotic formula for the partial derivatives of the Maass–Poincaré series with respect to y as well as extending an asymptotic for the growth of the ℓth repeated integral of the Gauss error function at x to include ℓ∈\R and a wider range of x. | - |
dc.language | eng | en_US |
dc.relation.ispartof | Mathematical Research Letters | en_US |
dc.title | Faber polynomials and poincaré series | en_US |
dc.title | Faber polynomials and poincare series | - |
dc.type | Article | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.4310/MRL.2011.v18.n4.a2 | - |
dc.identifier.scopus | eid_2-s2.0-80051970935 | en_US |
dc.identifier.volume | 18 | en_US |
dc.identifier.issue | 4 | en_US |
dc.identifier.spage | 591 | en_US |
dc.identifier.epage | 611 | en_US |
dc.identifier.issnl | 1073-2780 | - |