English

On sign changes for almost prime coefficients of half-integral weight modular forms

Number Theory 2016-03-22 v2

Abstract

For a half-integral weight modular form f=n=1af(n)nk12qnf = \sum_{n=1}^{\infty} a_f(n)n^{\frac{k-1}{2}} q^n of weight k=l+12k = l +\frac{1}{2} on Γ0(4)\Gamma_0(4) such that af(n)a_f(n) (nn \in N\mathbb{N}) are real, we prove for a fixed suitable natural number rr that af(n)a_f(n) changes sign infinitely often as nn varies over numbers having at most rr prime factors, assuming the analog of the Ramanujan conjecture for half-integral weight forms.

Keywords

Cite

@article{arxiv.1504.03948,
  title  = {On sign changes for almost prime coefficients of half-integral weight modular forms},
  author = {Srilakshmi Krishnamoorthy and M. Ram Murty},
  journal= {arXiv preprint arXiv:1504.03948},
  year   = {2016}
}

Comments

To appear in Mathematika

R2 v1 2026-06-22T09:16:36.053Z