关于符号变化的简短说明
A short note on sign changes
摘要：
本文给出了满模群$SL_2(\mathbb{Z})$的正规化Hecke特征尖点形式的傅里叶系数序列$\{a(n^j)\}_{n\ge 1}, j=2,3,4$的符号变化数的一个定量结果.对于同余子群$N$为无平方数的$Γ_0(N)$，我们还证明了某些广义模函数的$q$ -指数$c(p) (p {vary over primes})$符号变化数的类似定量结果.
英文摘要：
In this paper, we present a quantitative result for the number of sign changes for the sequences $\{a(n^j)\}_{n\ge 1}, j=2,3,4$ of the Fourier coefficients of normalized Hecke eigen cusp forms for the full modular group $SL_2(\mathbb{Z})$. We also prove a similar kind of quantitative result for the number of sign changes of the $q$-exponents $c(p) (p {vary over primes})$ of certain generalized modular functions for the congruence subgroup $Γ_0(N)$, where $N$ is square-free.
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