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Article: Subconvexity bounds for Rankin-Selberg L-functions for congruence subgroups

TitleSubconvexity bounds for Rankin-Selberg L-functions for congruence subgroups
Authors
Issue Date2006
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt
Citation
Journal Of Number Theory, 2006, v. 121 n. 2, p. 204-223 How to Cite?
AbstractEstimation of shifted sums of Fourier coefficients of cusp forms plays crucial roles in analytic number theory. Its known region of holomorphy and bounds, however, depend on bounds toward the general Ramanujan conjecture. In this article, we extended such a shifted sum meromorphically to a larger half plane Re s > 1 / 2 and proved a better bound. As an application, we then proved a subconvexity bound for Rankin-Selberg L-functions which does not rely on bounds toward the Ramanujan conjecture: Let f be either a holomorphic cusp form of weight k, or a Maass cusp form with Laplace eigenvalue 1 / 4 + k2, for Γ0 (N). Let g be a fixed holomorphic or Maass cusp form. What we obtained is the following bound for the L-function L (s, f ⊗ g) in the k aspect:L (1 / 2 + i t, f ⊗ g) ≪ k1 - 1 / (8 + 4 θ) + ε, where θ is from bounds toward the generalized Ramanujan conjecture. Note that a trivial θ = 1 / 2 still yields a subconvexity bound. © 2006 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75425
ISSN
2015 Impact Factor: 0.596
2015 SCImago Journal Rankings: 0.858
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_HK
dc.contributor.authorLiu, Jen_HK
dc.contributor.authorYe, Yen_HK
dc.date.accessioned2010-09-06T07:10:59Z-
dc.date.available2010-09-06T07:10:59Z-
dc.date.issued2006en_HK
dc.identifier.citationJournal Of Number Theory, 2006, v. 121 n. 2, p. 204-223en_HK
dc.identifier.issn0022-314Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/75425-
dc.description.abstractEstimation of shifted sums of Fourier coefficients of cusp forms plays crucial roles in analytic number theory. Its known region of holomorphy and bounds, however, depend on bounds toward the general Ramanujan conjecture. In this article, we extended such a shifted sum meromorphically to a larger half plane Re s > 1 / 2 and proved a better bound. As an application, we then proved a subconvexity bound for Rankin-Selberg L-functions which does not rely on bounds toward the Ramanujan conjecture: Let f be either a holomorphic cusp form of weight k, or a Maass cusp form with Laplace eigenvalue 1 / 4 + k2, for Γ0 (N). Let g be a fixed holomorphic or Maass cusp form. What we obtained is the following bound for the L-function L (s, f ⊗ g) in the k aspect:L (1 / 2 + i t, f ⊗ g) ≪ k1 - 1 / (8 + 4 θ) + ε, where θ is from bounds toward the generalized Ramanujan conjecture. Note that a trivial θ = 1 / 2 still yields a subconvexity bound. © 2006 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnten_HK
dc.relation.ispartofJournal of Number Theoryen_HK
dc.titleSubconvexity bounds for Rankin-Selberg L-functions for congruence subgroupsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022-314X&volume=121&spage=204&epage=223&date=2006&atitle=Subconvexity+bounds+for+Rankin-Selberg+L-functions+for+congruence+subgroupsen_HK
dc.identifier.emailLau, YK:yklau@maths.hku.hken_HK
dc.identifier.authorityLau, YK=rp00722en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jnt.2006.02.006en_HK
dc.identifier.scopuseid_2-s2.0-33748926601en_HK
dc.identifier.hkuros127738en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33748926601&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume121en_HK
dc.identifier.issue2en_HK
dc.identifier.spage204en_HK
dc.identifier.epage223en_HK
dc.identifier.isiWOS:000242688000002-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridLau, YK=35724053400en_HK
dc.identifier.scopusauthoridLiu, J=7410107044en_HK
dc.identifier.scopusauthoridYe, Y=7401627512en_HK

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