### Abstract

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.

Original language | English |
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Pages (from-to) | 77-88 |

Number of pages | 12 |

Journal | Lithuanian Mathematical Journal |

Volume | 38 |

Issue number | 1 |

Publication status | Published - 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**An application of the mellin-barnes type of integral to the mean square of l-functions.** / Katsurada, Masanori.

Research output: Contribution to journal › Article

*Lithuanian Mathematical Journal*, vol. 38, no. 1, pp. 77-88.

}

TY - JOUR

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

AU - Katsurada, Masanori

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.

UR - http://www.scopus.com/inward/record.url?scp=54649084734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54649084734&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:54649084734

VL - 38

SP - 77

EP - 88

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 1

ER -