Dirichlet series associated with square of class numbers of binary quadratic forms

Mizuno Y.

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Dirichlet series associated with square of class numbers of binary quadratic forms

机译：Dirichlet级数与二进制二次型的类号的平方相关

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摘要

We give meromorphic continuations and functional equations of Mellin transform and Rankin-Selberg convolution associated with a real analytic Eisenstein series of half-integral weight. Applications to Dirichlet series whose coefficients are the class numbers of binary quadratic forms are given.

机译：我们给出了与实际的半积分权重的爱森斯坦级数解析相关的梅林变换和兰金-塞尔伯格卷积的亚纯连续性和泛函方程。给出了Dirichlet级数的应用，其系数为二进制二次形式的类数。

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来源
《Mathematische Zeitschrift》 |2012年第4期|共21页
作者
Mizuno Y.;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Class numbers; Koecher-Maass series; Shintani zeta functions; Siegel-Eisenstein series;

机译：类编号;Koecher-Maass系列;Shintani zeta函数;Siegel-Eisenstein系列;

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专利

1. Dirichlet series associated with square of class numbers of binary quadratic forms [J] . Mizuno Y. Mathematische Zeitschrift . 2012,第3a4期

机译：Dirichlet级数与二进制二次型的类号的平方相关
2. RELATIONS AMONG DIRICHLET SERIES WHOSE COEFFICIENTS ARE CLASS NUMBERS OF BINARY CUBIC FORMS II [J] . Yasuo Ohno, Takashi Taniguchi Mathematical research letters: MRL . 2014,第2期

机译：Dirichlet系列之间的关系，它们是二元立方型的分类号II
3. RELATIONS AMONG DIRICHLET SERIES WHOSE COEFFICIENTS ARE CLASS NUMBERS OF BINARY CUBIC FORMS [J] . Ohno Y, Taniguchi T, Wakatsuki S American Journal of Mathematics . 2009,第6期

机译：Dirichlet级数之间的关系是二元立方型的类数
4. Dirichlet Series for Squares of Sums of Squares: A Summary [C] . Jonathan Michael Bonvein, Kwok-Kwong Stephen Choi Canadian Number Theory Association . 2004

机译：Dirichlet系列用于平方和正方形的正方形：摘要
5. An algorithmic solution to the representation problem for definite binary quadratic forms [D] . Jameson, Eric Joseph. 2016

机译：定二进制二次形式表示问题的算法解决方案
6. Overpartitions and class numbers of binary quadratic forms [O] . Kathrin Bringmann, Jeremy Lovejoy 2009

机译：二进制二次形式的分区和类号
7. On Dirichlet series whose coefficients are class numbers of binary quadratic forms [O] . Boris A. Datskovsky 1996

机译：在Dirichlet系列上，其系数是二元二次形式的类数

Dirichlet series associated with square of class numbers of binary quadratic forms

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