华东师范大学学报（自然科学版） >

2017 , Vol. 2017 >Issue 6: 1 - 24

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.06.001

数学

由几何级数的扭曲生成的艾森斯坦级数

  • 沈力健
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  • 佛罗里达大学 数学系, 盖恩斯维尔 佛罗里达 32611-8105, 美国
沈力健,男,教授,研究方向为函数论.E-mail:shen@ufl.edu

收稿日期: 2017-03-29

  网络出版日期: 2017-11-25

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On Eisenstein series generated from twisting of the geometric series

  • SHEN Li-chien
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  • Department of Mathematics, University of Florida, Gainesville FL 32611-8105, USA

Received date: 2017-03-29

  Online published: 2017-11-25

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摘要

本文借助狄利克雷特征处理了几何级数的扭曲.结合傅里叶变换的基本工具，生成了一族算术群的所有艾森斯坦级数.

关键词： 狄利克雷特征; 导子; 艾森斯坦级数; 高斯和; 克罗内克符号; 梅林变换; 模形式; 泊松求和公式; 韦伊逆定理

本文引用格式

沈力健 . 由几何级数的扭曲生成的艾森斯坦级数[J]. 华东师范大学学报（自然科学版）, 2017 , 2017(6) : 1 -24 . DOI: 10.3969/j.issn.1000-5641.2017.06.001

Abstract

In this paper, we will be dealing with the twisting of geometric series by the Dirichlet characters. In conjunction with the basic tool of Fourier transform, it can be used to generate all the Eisenstein series with respect to a family arithmetic groups.

Key words： Dirichlet character; conductor; Eisenstein series; Gaussian sum; Kronecker symbol; Mellin transform; modular form; Poisson summation formula; Weil's converse theorem

参考文献

[1] BUMP D. Automorphic Forms and Representations[M]. Cambridge:Cambridge University Press, 1997.
[2] COHN H. Advanced Number Theory[M]. New York:Dover, 1980.
[3] BOREVICH Z I, SHAFAREVICH I R. Number Theory[M]. New York:Academic Press, 1966.
[4] SHEN L C. On the modular equations of degree 3[J]. Proceedings of AMS, 1994, 122(4):1101-1114.
[5] SHEN L C. On a class of q-series related to quadratic forms[J]. Bulletin of the Institute of Mathematics Academia Sinica, 1998, 26(2):111-126.
[6] KOBLITZ N. Introduction to Elliptic Curves and Modular Forms[M]. 2nd ed. New York:Springer-Verlag, 1993.
[7] DIAMOND F, SHURMAN J. A First Course in Modular Forms[M]. Berlin:Springer, 2005.
[8] WEIL A. Elliptic Functions According to Eisenstein and Kronecker[M]. Berlin:Springer-Verlag, 1976.
[9] WHITTAKER E T, WATSON G N. A Curse of Modern Analysis[M]. 4th ed. Cambridge:Cambridge University Press, 1958.
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