An infinite family of vector-valued mock theta functions

被引：0

作者：

Andersen, Nickolas ^{[1
]}

Williams, Clayton ^{[2
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Univ Illinois, Dept Math, Urbana, IL USA

来源：

RAMANUJAN JOURNAL | 2024年 / 65卷 / 04期

关键词：

Mock theta functions; Weil representation; Vector-valued forms; Modular forms; Maass forms; Mock modular forms; DYSONS RANKS; PROOF;

D O I：

10.1007/s11139-023-00745-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We exhibit an infinite family of vector-valued mock theta functions indexed by positive integers coprime to 6. These are built from specializations of Dyson's rank generating function and related functions studied by Watson, Gordon, and McIntosh. The associated completed harmonic Maass forms transform according to the Weil representation attached to a rank one lattice. This strengthens a 2010 result of Bringmann and Ono and a 2019 result of Garvan.

引用

页码：1813 / 1825

页数：13

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