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 be the coefficient of in its series expansion. We say that g is of parity type if takes even values with probability a for . We show that among the 44 classical mock theta functions, 21 of them are of parity type . We further conjecture that 19 mock theta functions are of parity type and 4 functions are of parity type . We also give characterizations of n such that is odd for the mock theta functions of parity type .
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 是系数 在其系列扩展中。我们说g是奇偶校验类型 如果 即使需要用值概率一对. 我们表明,在 44 个经典模拟 theta 函数中,其中 21 个是奇偶类型. 我们进一步推测 19 个模拟 theta 函数是奇偶类型 和 4 个函数是奇偶校验类型 . 我们还给出了n 的特征,使得 奇偶校验类型的模拟 theta 函数是奇数 .