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Article: A new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroups

TitleA new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroups
Authors
Issue Date2006
PublisherOxford University Press. The Journal's web site is located at http://imrp.oxfordjournals.org
Citation
International Mathematics Research Papers, 2006, v. 2006 How to Cite?
AbstractLet f be a holomorphic Hecke eigenform for Γ0(N) of weight k, or a Maass eigenform for Γ0(N) with Laplace eigenvalue 1/4 + k2. Let g be a fixed holomorphic or Maass cusp form for Γ0(N). A subconvexity bound for central values of the Rankin-Selberg L-function L(s, f ⊗ g) is proved in the k-aspect: L(1/2 + it, f ⊗ g) ≪N,g,t,ε k2/3+ε, while a convexity bound is only ≪ k1+ε. The dependence of the implied constant on t and the level N is polynomial. This new bound improves earlier subconvexity bounds for these Rankin-Selberg L-functions by Sarnak, the authors, and Blomer. Techniques used include a result of Good, spectral large sieve, meromorphic continuation of a shifted convolution sum to Res > -1/2 passing through all Laplace eigenvalues, and a weighted stationary phase argument.
Persistent Identifierhttp://hdl.handle.net/10722/156169
ISSN
2010 Impact Factor: 0.2
2009 SCImago Journal Rankings: 0.476
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLau, YKen_US
dc.contributor.authorLiu, Jen_US
dc.contributor.authorYe, Yen_US
dc.date.accessioned2012-08-08T08:40:41Z-
dc.date.available2012-08-08T08:40:41Z-
dc.date.issued2006en_US
dc.identifier.citationInternational Mathematics Research Papers, 2006, v. 2006en_US
dc.identifier.issn1687-3017en_US
dc.identifier.urihttp://hdl.handle.net/10722/156169-
dc.description.abstractLet f be a holomorphic Hecke eigenform for Γ0(N) of weight k, or a Maass eigenform for Γ0(N) with Laplace eigenvalue 1/4 + k2. Let g be a fixed holomorphic or Maass cusp form for Γ0(N). A subconvexity bound for central values of the Rankin-Selberg L-function L(s, f ⊗ g) is proved in the k-aspect: L(1/2 + it, f ⊗ g) ≪N,g,t,ε k2/3+ε, while a convexity bound is only ≪ k1+ε. The dependence of the implied constant on t and the level N is polynomial. This new bound improves earlier subconvexity bounds for these Rankin-Selberg L-functions by Sarnak, the authors, and Blomer. Techniques used include a result of Good, spectral large sieve, meromorphic continuation of a shifted convolution sum to Res > -1/2 passing through all Laplace eigenvalues, and a weighted stationary phase argument.en_US
dc.languageengen_US
dc.publisherOxford University Press. The Journal's web site is located at http://imrp.oxfordjournals.orgen_US
dc.relation.ispartofInternational Mathematics Research Papersen_US
dc.titleA new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroupsen_US
dc.typeArticleen_US
dc.identifier.emailLau, YK:yklau@maths.hku.hken_US
dc.identifier.authorityLau, YK=rp00722en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1155/IMRP/2006/35090en_US
dc.identifier.scopuseid_2-s2.0-33749676055en_US
dc.identifier.hkuros125023-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33749676055&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume2006en_US
dc.identifier.eissn1687-3009-
dc.identifier.isiWOS:000240186800001-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLau, YK=35724053400en_US
dc.identifier.scopusauthoridLiu, J=7410107044en_US
dc.identifier.scopusauthoridYe, Y=7401627512en_US

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