Quantum mock modular forms arising from eta–theta functions
Quantum mock modular forms arising from eta–theta functions
复制标题
由 eta-theta 函数产生的量子模拟模块化形式
DOI：
10.1007/s40993-016-0045-7
复制
发表时间：
2016
影响因子：
0.8
通讯作者：
Stephanie Treneer
中科院分区：
文献类型：
--
作者：
A. Folsom;S. Garthwaite;Soon;H. Swisher;Stephanie Treneer
在2013年，Lemke奥利弗分类了所有的θ函数。本文通过由偶数特征的eta-theta函数构造mock模形式来统一eta-theta函数，使得这些mock模形式的影子由奇数特征的eta-theta函数给出.此外，我们证明了我们的模拟模形式是量子模形式。作为推论，我们建立了简单的有限超几何表达式，可用于评估Eichler积分的奇数eta-theta函数，以及一些奇怪的代数身份。
In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even characters, such that the shadows of these mock modular forms are given by the eta–theta functions with odd characters. In addition, we prove that our mock modular forms are quantum modular forms. As corollaries, we establish simple finite hypergeometric expressions which may be used to evaluate Eichler integrals of the odd eta–theta functions, as well as some curious algebraic identities.