File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1155/IMRP/2006/35090
- Scopus: eid_2-s2.0-33749676055
- WOS: WOS:000240186800001
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: A new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroups
Title | A new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroups |
---|---|
Authors | |
Issue Date | 2006 |
Publisher | Oxford 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? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/156169 |
ISSN | 2010 Impact Factor: 0.200 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Lau, YK | en_US |
dc.contributor.author | Liu, J | en_US |
dc.contributor.author | Ye, Y | en_US |
dc.date.accessioned | 2012-08-08T08:40:41Z | - |
dc.date.available | 2012-08-08T08:40:41Z | - |
dc.date.issued | 2006 | en_US |
dc.identifier.citation | International Mathematics Research Papers, 2006, v. 2006 | en_US |
dc.identifier.issn | 1687-3017 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156169 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.publisher | Oxford University Press. The Journal's web site is located at http://imrp.oxfordjournals.org | en_US |
dc.relation.ispartof | International Mathematics Research Papers | en_US |
dc.title | A new bound k2/3+ε for Rankin-Selberg L-functions for Hecke congruence subgroups | en_US |
dc.type | Article | en_US |
dc.identifier.email | Lau, YK:yklau@maths.hku.hk | en_US |
dc.identifier.authority | Lau, YK=rp00722 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1155/IMRP/2006/35090 | en_US |
dc.identifier.scopus | eid_2-s2.0-33749676055 | en_US |
dc.identifier.hkuros | 125023 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33749676055&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 2006 | en_US |
dc.identifier.eissn | 1687-3009 | - |
dc.identifier.isi | WOS:000240186800001 | - |
dc.publisher.place | United Kingdom | en_US |
dc.identifier.scopusauthorid | Lau, YK=35724053400 | en_US |
dc.identifier.scopusauthorid | Liu, J=7410107044 | en_US |
dc.identifier.scopusauthorid | Ye, Y=7401627512 | en_US |
dc.identifier.issnl | 1687-3009 | - |