Comparing Hecke eigenvalues of newforms

被引：9
作者：
Chiriac, Liubomir [1 ]
机构：
[1] Univ Massachusetts, Dept Math & Stat, 710 N Pleasant St, Amherst, MA 01003 USA
来源：
ARCHIV DER MATHEMATIK | 2017年 / 109卷 / 03期
关键词：
Hecke eigenvalues of newforms; Symmetric power L-functions; Cuspidal automorphic representations; MULTIPLICITY ONE;
D O I：
10.1007/s00013-017-1072-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given two distinct newforms with real Fourier coefficients, we show that the set of primes where the Hecke eigenvalues of one of them dominate the Hecke eigenvalues of the other has density 1/16. Furthermore, if the two newforms do not have complex multiplication, and neither is a quadratic twist of the other, we also prove a similar result for the squares of their Hecke eigenvalues.
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收藏
页码：223 / 229
页数：7
相关论文
共 7 条
[1]  
[Anonymous], CRM P LECT NOTES
[2]  
GELBART S, 1978, ANN SCI ECOLE NORM S, V11, P471
[3]  
Kim HH, 2002, DUKE MATH J, V112, P177
[4]   On modular signs [J].
Kowalski, E. ;
Lau, Y-K. ;
Soundararajan, K. ;
Wu, J. .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2010, 149 :389-411
[5]   On signs of Fourier coefficients of cusp forms [J].
Matomaki, Kaisa .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2012, 152 :207-222
[6]   Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2) [J].
Ramakrishnan, D .
ANNALS OF MATHEMATICS, 2000, 152 (01) :45-111
[7]   APPENDIX - A REFINEMENT OF THE STRONG MULTIPLICITY ONE THEOREM FOR GL(2) [J].
RAMAKRISHNAN, D .
INVENTIONES MATHEMATICAE, 1994, 116 (1-3) :645-649
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