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:
Mathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United StatesMathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United States
Chandee, Vorrapan
Li, Xiannan
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机构:
Mathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United StatesMathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United States
Li, Xiannan
Matomäki, Kaisa
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机构:
Department of Mathematics and Statistics, University of Turku, Turku,20014, FinlandMathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United States
Matomäki, Kaisa
Radziwill, Maksym
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机构:
Department of Mathematics, Lunt Hall, 2033 Sheridan Road, Evanston,IL,60208, United StatesMathematics Department, 138 Cardwell Hall, Manhattan,KS,66506, United States