A converse theorem for double Dirichlet series and Shintani zeta functions

Nikolaos Diamantis; Dorian Goldfeld

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A converse theorem for double Dirichlet series and Shintani zeta functions

机译：双重Dirichlet级数和Shintani zeta函数的逆定理

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摘要

A converse theorem for double Dirichlet series is established. As an application, we show that certain zeta functions introduced by Shintani are actually Weyl group multiple Dirichlet series associated to metaplectic Eisenstein series on GL(2).

机译：建立了双Dirichlet级数的逆定理。作为应用，我们证明了Shintani引入的某些zeta函数实际上是与GL（2）上的全辛爱森斯坦级数相关的Weyl群多重Dirichlet级数。

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来源
《Journal of the Mathematical Society of Japan》 |2014年第2期|449-477|共29页
作者
Nikolaos Diamantis; Dorian Goldfeld;
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作者单位

Max-Planck-Institut fuer Mathematik Vivatsgasse 7 53111 Bonn, Germany, School of Mathematical Sciences University of Nottingham Nottingham NG7 2RD, UK;

Department of Mathematics Columbia University New York NY 10027, USA;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
double Dirichlet series; Eisenstein series; converse theorems; forms of half-integral weight;

机译：双Dirichlet系列;爱森斯坦系列;逆定理半积分重量的形式;

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专利

1. Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series [J] . Kohji Matsumoto Nagoya Mathematical Journal . 2003,第2期

机译：Barnes，Shintani和Eisenstein系列的双重zeta函数的渐近展开
2. A converse theorem for double Dirichlet series [J] . Diamantis N., Goldfeld D. American Journal of Mathematics . 2011,第4期

机译：双重Dirichlet级数的逆定理
3. Uniform distribution of the zeros of the Riemann zeta function and the mean value theorems of Dirichlet $L$-functions [J] . Akio Fujii Proceedings of the Japan Academy, Series A. Mathematical Sciences . 1987,第9期

机译：黎曼zeta函数零点的均匀分布和Dirichlet $ L $-函数的均值定理
4. Asymptotic expansions for double Shintani zeta‐functions of several variables [C] . Masanori Katsurada Conference on Diophantine Analysis and Related Fields . 2011

机译：几种变量的双神坦Zeta函数的渐近扩展
5. ZETA(S,A,X) AND GENERALIZED DIRICHLET SERIES WITH EMPHASIS ON LOCATION OF ZEROS. [D] . GRINSTEIN, GEORGES GREGOREVITCH. 1977

机译：ZETA（S，A，X）和广义Dirichlet系列，着重于ZEROS的位置。
6. ω-Theorems for Quotients of Zeta-Functions at Combinations of Points [O] . Norman Levinson 1972

机译：点组合下的Zeta函数商的ω-定理
7. A converse theorem for double Dirichlet series and Shintani zeta functions [O] . Diamantis Nikolaos, Goldfeld Dorian 2014

机译：双重Dirichlet级数和Shintani zeta函数的逆定理

A converse theorem for double Dirichlet series and Shintani zeta functions

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