Monotone Chains in Modulus of Two Classes of Dirichlet Coefficients  

作　　者：Guang Shi Lü Qiang MA 

机构地区：[1]School of Mathematics,Shandong University,Ji'nan 250100,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第6期1101-1114,共14页数学学报（英文版）

基　　金：Supported by the National Key Research and Development Program of China(Grant No.2021YFA1000700);NSFC(Grant No.12031008)。

摘　　要：Let f1,...,fkand g1,...,qkbe non-CM newforms of square-free levels.Denote byλ_(sym)jf_(i)(n)the coefficients of the Dirichlet expansion of L(sym^(j)f_(i),s)andν1,...,νkthe distinct positive integers such thatλ_(sym)jf_(i)(νi)≠0.In this paper,we obtain that there exist infinitely many positive integers m such that 0<λ_(sym)jf_(1)(m+ν1)|<|λ_(sym)jf_(2)(m+ν2)|<…<|λ_(sym)jf_(k)(m+νk)|.For coefficients of the Dirichlet expansion of L(sym^(j1)f×sym^(j2)g,s),we have a similar result.

关 键 词：Dirichlet coefficients Sato-Tate conjecture 

分 类 号：O153.3[理学—数学]