TY - JOUR

T1 - An application of the mellin-barnes type of integral to the mean square of l-functions

AU - Katsurada, M.

N1 - Funding Information:
Research supported by Grant-in-Aid for Scientific Research (No. 07740035), Ministry of Education, Science, Sports, and Culture, Japan.

PY - 1998

Y1 - 1998

N2 - The mean square of all Dirichlet L-functions (mod q), in the form (2.1) given below, will be investigated. We establish full asymptotic expansions for (2.1) (see Theorems 1 and 2) by introducing the Mellin-Bames type of integral formula (3.4) for the infinite double sum (3.2). Our treatment of (2.1) becomes, by virtue of (3.4), considerably simpler than the existing methods. Further improvements (Theorems A and B) are also given.

AB - The mean square of all Dirichlet L-functions (mod q), in the form (2.1) given below, will be investigated. We establish full asymptotic expansions for (2.1) (see Theorems 1 and 2) by introducing the Mellin-Bames type of integral formula (3.4) for the infinite double sum (3.2). Our treatment of (2.1) becomes, by virtue of (3.4), considerably simpler than the existing methods. Further improvements (Theorems A and B) are also given.

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U2 - 10.1007/BF02465546

DO - 10.1007/BF02465546

M3 - Article

AN - SCOPUS:54649084734

SN - 0363-1672

VL - 38

SP - 77

EP - 88

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

IS - 1

ER -