华东师范大学学报（自然科学版） >

2019 , Vol. 2019 >Issue 2: 7 - 20

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.02.002

数学

与虚二次域相关的权为1的艾森斯坦级数

  • 沈力健
展开
  • 佛罗里达大学 数学系, 盖恩斯维尔 FL 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: 2018-02-07

  网络出版日期: 2019-03-27

收起

Weight one Eisenstein series associated with imaginary quadratic fields

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

Received date: 2018-02-07

  Online published: 2019-03-27

Fold

摘要

考虑了一类与虚二次域相关的权为1的艾森斯坦级数.与克罗内克符号相关的艾森斯坦级数的子空间由高斯亏格理论产生的二次型刻画.此外，我们给出了一系列与二次域相关的恒等式.

关键词： 艾森斯坦级数; 克罗内克符号; 判别式; 二次域; 模形式

本文引用格式

沈力健 . 与虚二次域相关的权为1的艾森斯坦级数[J]. 华东师范大学学报（自然科学版）, 2019 , 2019(2) : 7 -20 . DOI: 10.3969/j.issn.1000-5641.2019.02.002

Abstract

We consider a family of weight one Eisenstein series associated with the imaginary quadratic fields. The subspace of the Eisenstein series associated with the Kronecker symbol is characterized by the quadratic forms generated from the genus theory of Gauss; we will derive a family of identities connected with these quadratic fields.

Key words： Eisenstein series; Kronecker symbol; discriminant; quadratic field; modular form

参考文献

[1] COHN H. Advanced Number Theory[M]. New York:Dover, 1980.
[2] BOREVICH Z I, SHAFAREVICH I R. Number Theory[M]. New York:Academic Press, 1966.
[3] SHEN L C. On Eisenstein series generated from twisting of the geometric series[J]. Journal of East China Normal University (Natural Science), 2017, 6:1-24.
[4] 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.
[5] SIEGEL C L. Lectures on Advanced Analytic Number Theory[M]. Bombay:Tata Institute, 1961.
[6] SHEN L C. On separation of quadratic forms on the imaginary quadratic field in its Hilbert class fields[J]. Proceedings of the American Mathematical Society, 2008, 136(9):3061-3067.
[7] DIAMOND F, SHURMAN J. A First Course in Modular Forms[M]. New York:Springer, 2005.
[8] COX D. Primes of the forms x2 +ny2[M]//Fermat, Class Field Theory, and Complex Multiplication. New York:Wiley, 1989.
[9] KOBLITZ N. Introduction to Elliptic Curves and Modular Forms[M]. 2nd ed. New York:Springer-Verlag, 1993.
Options
文章导航

/

〈 〉