Journal article
Zero density for automorphic L-functions
Journal of number theory, Vol.133(11), pp.3877-3901
11/2013
DOI: 10.1016/j.jnt.2013.05.012
Abstract
In this paper, zero density estimates for automorphic L-functions L(s,π) for GLn are deduced from a bound for an integral power moment of L(s,π) on the critical line Re(s)=1/2. In particular for the Riemann zeta function, classical zero density estimates are extended to short vertical strips. For g being a holomorphic or Maass eigenform for SL2(Z), bounds for zero density for L(s,g) in short strips are proved, which extend Ivićʼs results on long strips. For a self-dual Hecke Maass eigenform f for SL3(Z), estimates of zero density for L(s,f) in short and long strips are also proved. The proofs use a zero detecting argument, a large sieve inequality, a bound for an integral power moment of L(1/2+it,π), the Rankin–Selberg theory, and the Halász–Montgomery–Jutila method.
Details
- Title: Subtitle
- Zero density for automorphic L-functions
- Creators
- Yangbo Ye - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USADeyu Zhang - School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, China
- Resource Type
- Journal article
- Publication Details
- Journal of number theory, Vol.133(11), pp.3877-3901
- DOI
- 10.1016/j.jnt.2013.05.012
- ISSN
- 0022-314X
- eISSN
- 1096-1658
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11001154; DOI: 10.13039/501100007129, name: Natural Science Foundation of Shandong Province, award: ZR2010AQ009
- Language
- English
- Date published
- 11/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9983985866102771
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