RANKIN-SELBERG METHOD FOR JACOBI FORMS OF INTEGRAL WEIGHT AND OF HALF-INTEGRAL WEIGHT ON SYMPLECTIC GROUPS

IF 0.6 4区 数学 Q3 MATHEMATICS Kyushu Journal of Mathematics Pub Date : 2018-04-12 DOI:10.2206/kyushujm.73.391
S. Hayashida
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引用次数: 1

Abstract

In this article we show analytic properties of certain Rankin-Selberg type Dirichlet series for holomorphic Jacobi cusp forms of integral weight and of half-integral weight. The numerators of these Dirichlet series are the inner products of Fourier-Jacobi coefficients of two Jacobi cusp forms. The denominators and the range of summation of these Dirichlet series are like the ones of the Koecher-Maass series. The meromorphic continuations and functional equations of these Dirichlet series are obtained. Moreover, an identity between the Petersson norms of Jacobi forms with respect to linear isomorphism between Jacobi forms of integral weight and half-integral weight is also obtained.
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辛群上积分权和半积分权JACOBI形式的RANKIN-SELBERG方法
本文给出了积分权和半积分权的全纯Jacobi尖点形式的某些Rankin-Selberg型Dirichlet级数的解析性质。这些狄利克雷级数的分子是两个雅可比尖点形式的傅立叶-雅可比系数的内积。这些狄利克雷级数的分母和求和范围类似于Koecher-Maas级数。得到了这些Dirichlet级数的亚纯延拓和函数方程。此外,关于积分权和半积分权的Jacobi形式之间的线性同构,还得到了Jacobi形式的Petersson范数之间的恒等式。
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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