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Parity of coefficients of mock theta functions
Journal of Number Theory ( IF 0.7 ) Pub Date : 2021-06-01 , DOI: 10.1016/j.jnt.2021.04.023
Liuquan Wang

We study the parity of coefficients of classical mock theta functions. Suppose g is a formal power series with integer coefficients, and let c(g;n) be the coefficient of qn in its series expansion. We say that g is of parity type (a,1a) if c(g;n) takes even values with probability a for n0. We show that among the 44 classical mock theta functions, 21 of them are of parity type (1,0). We further conjecture that 19 mock theta functions are of parity type (12,12) and 4 functions are of parity type (34,14). We also give characterizations of n such that c(g;n) is odd for the mock theta functions of parity type (1,0).



中文翻译:

模拟 theta 函数系数的奇偶校验

我们研究经典模拟 theta 函数系数的奇偶性。假设g是一个具有整数系数的形式幂级数,让C(G;n) 是系数 qn在其系列扩展中。我们说g是奇偶校验类型(一种,1-一种) 如果 C(G;n)即使需要用值概率n0. 我们表明,在 44 个经典模拟 theta 函数中,其中 21 个是奇偶类型(1,0). 我们进一步推测 19 个模拟 theta 函数是奇偶类型(12,12) 和 4 个函数是奇偶校验类型 (34,14). 我们还给出了n 的特征,使得C(G;n) 奇偶校验类型的模拟 theta 函数是奇数 (1,0).

更新日期:2021-06-11
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