The fourth moment of derivatives of Dirichlet L-functions in function fields

被引:1
|
作者
Andrade, Julio Cesar [1 ]
Yiasemides, Michael [1 ]
机构
[1] Univ Exeter, Dept Math, Exeter EX4 4QF, Devon, England
基金
英国工程与自然科学研究理事会;
关键词
Moments of L-functions; Dirichlet character; Polynomial; Function field; Derivative; EULER-HADAMARD PRODUCT; ZETA-FUNCTION; MEAN-VALUE; ZEROS; POLYNOMIALS; THEOREMS; VALUES;
D O I
10.1007/s00209-020-02673-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We obtain the asymptotic main term of moments of arbitrary derivatives of L-functions in the function field setting. Specifically, we obtain the first, second, and mixed fourth moments. The average is taken over all non-trivial characters of a prime modulus Q is an element of F-q[T], and the asymptotic limit is as deg Q -> infinity. This extends the work of Tamam who obtained the asymptotic main term of low moments of L-functions, without derivatives, in the function field setting. It is also the function field q-analogue of the work of Conrey, who obtained the fourth moment of derivatives of the Riemann zeta-function.
引用
收藏
页码:671 / 697
页数:27
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