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.
机构:
Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
Inst Adv Study, Sch Math, Princeton, NJ 08540 USAUniv Calif San Diego, Dept Math, La Jolla, CA 92093 USA
Bucur, Alina
Diaconu, Adrian
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机构:
Univ Minnesota, Sch Math, Minneapolis, MN 55455 USAUniv Calif San Diego, Dept Math, La Jolla, CA 92093 USA