On sign changes for almost prime coefficients of half-integral weight modular forms
classification
🧮 math.NT
keywords
weighthalf-integralchangesformsfracmodularprimesign
read the original abstract
For a half-integral weight modular form $f = \sum_{n=1}^{\infty} a_f(n)n^{\frac{k-1}{2}} q^n$ of weight $k = l +\frac{1}{2}$ on $\Gamma_0(4)$ such that $a_f(n)$ ($n$ $\in$ $\mathbb{N}$) are real, we prove for a fixed suitable natural number $r$ that $a_f(n)$ changes sign infinitely often as $n$ varies over numbers having at most $r$ prime factors, assuming the analog of the Ramanujan conjecture for half-integral weight forms.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.