论文标题
模拟theta函数系数的均等
Parity of coefficients of mock theta functions
论文作者
论文摘要
我们研究经典模拟theta函数系数的均等。假设$ g $是一个具有整数系数的正式电源系列，让$ c（g; n）$成为其系列扩展中$ q^n $的系数。我们说，如果$ c（g; n）$均为$ c（a，1-a）$的$ g $，则均匀$ a $ a $ a $ a $ a \ geq 0 $。我们表明，在44个古典模拟theta功能中，其中21个是奇偶校类型$（1,0）$。我们进一步推测19个模拟theta函数是平等类型$（\ frac {1} {2} {2}，\ frac {1} {2}）$，而4个功能是均等型$（\ frac {3} {3} {4} {4} {4} {4}，\ frac {1} {1} {4} {4} {4} {{4}）$。我们还提供$ n $的特征，使$ c（g; n）$对于奇偶校类型$（1,0）$的模拟theta功能很奇怪。
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 $q^n$ in its series expansion. We say that $g$ is of parity type $(a,1-a)$ if $c(g;n)$ takes even values with probability $a$ for $n\geq 0$. 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 $(\frac{1}{2},\frac{1}{2})$ and 4 functions are of parity type $(\frac{3}{4},\frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of parity type $(1,0)$.
