由几何级数的扭曲生成的艾森斯坦级数

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On Eisenstein series generated from twisting of the geometric series

Department of Mathematics, University of Florida, Gainesville FL 32611-8105, USA

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.
- 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
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.
- Dirichlet character /
- conductor /
- Eisenstein series /
- Gaussian sum /
- Kronecker symbol /
- Mellin transform /
- modular form /
- Poisson summation formula /
- Weil's converse theorem

[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. http://d.wanfangdata.com.cn/OAPaper/oai_arXiv.org_0907.1725
[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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