Eichler orders and Jacobi forms of squarefree level

被引：3

作者：

Li, Yan-Bin ^{[1
]}

Skoruppa, Nils-Peter ^{[1
,2
]}

Zhou, Haigang ^{[1
]}

机构：

[1] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

[2] Univ Siegen, Siegen, Germany

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 236卷

关键词：

Jacobi forms; Definite quaternion algebras; Eichler orders; Class numbers; Type numbers; Theta series; Eisenstein series;

D O I：

10.1016/j.jnt.2021.07.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For all Eichler orders with a same squarefree level in a definite quaternion algebra over the field of rational numbers, we prove that a weighted sum of Jacobi theta series associated to these orders is a Jacobi Eisenstein series. Multiply the Fourier coefficients of the latter by a power of 2 to get our modified Hurwitz class numbers. As its corollaries, the modified Hurwitz class numbers can be used to calculate the traces of Brandt matrices and the type number of the Eichler orders. (c) 2021 Elsevier Inc. All rights reserved.

引用

页码：349 / 387

页数：39

共 12 条

[1]

Alsina M., 2004, CRM MONOGRAPH SERIES, V22

[2]

[Anonymous], 1973, Lecture Notes in Math.

[3] COUNTING ZEROS IN QUATERNION ALGEBRAS USING JACOBI FORMS [J].

Boylan, Hatice ;

Skoruppa, Nils-Peter ;

Zhou, Haigang .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 371 (09) :6487-6509

[4]

Eichler M., 1966, Pure Appl. Math., V23

[5]

Eichler Martin, 1985, THEORY JACOBI FORMS, V55

[6]

Gross B., 1987, CMS C P, V7, P115

[7]

Lam T.Y., 2005, GRADUATE STUDIES MAT, V67

[8] ACTION OF CANONICAL INVOLUTION ON MODULAR FORMS OF WEIGHT-2 ON GAMMAO(M) [J].

PIZER, A .

MATHEMATISCHE ANNALEN, 1977, 226 (02) :99-116

[9]

PIZER AK, 1973, J REINE ANGEW MATH, V264, P76

[10]

Reiner I., 2003, MAXIMAL ORDERS, V28

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