同态模态的劳伦展开

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-11-27 DOI:10.1112/jlms.70036

Gabriele Bogo, Yingkun Li, Markus Schwagenscheidt

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引用次数: 0

摘要

在本文中，我们通过给出两种计算方法，研究了复乘点处合模态形式的劳伦系数。第一种是对 Rodriguez-Villegas 和 Zagier 方法的推广，将劳伦系数表示为通过递归得到的多项式族的常数项。第二种方法适用于属于正则化 Theta 抬高的微模态形式，用谐波 Maass 形式的傅里叶系数来表示它们的洛朗系数。

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Laurent expansions of meromorphic modular forms

In this paper, we study the Laurent coefficients of meromorphic modular forms at complex multiplication points by giving two approaches of computing them. The first is a generalization of the method of Rodriguez-Villegas and Zagier, which expresses the Laurent coefficients as constant terms of a family of polynomials obtained through recursion. The second applies to meromorphic modular forms that are regularized theta lifts, and expresses their Laurent coefficients in terms of Fourier coefficients of harmonic Maass forms.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.