A note on the extended Bruinier-Kohnen conjecture

Abstract

Let $f$ be a cuspform of integral half-weight $k+1/2$, whose Fourier coefficients $a(n)$ not necessarily real. We verify partially an extension of a conjecture of Bruinier and Kohnen on the equi-distribution of the signs of $a(n)$ (when are real), conjectured by the first author in \cite{Amri2} for the sequence $\{a(t{p}^{2\nu }){\}}_{p,\text{prime}}$, where $\nu$ an odd positive integer and $t$ a square-free integer.

References in corpus (6)

• On conjectures of Sato-Tate and Bruinier-Kohnen
• Equidistribution of Signs for Modular Eigenforms of Half Integral Weight
• A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and Halász' Theorem
• Simultaneous sign change and equidistribution of signs of Fourier coefficients of two cusp forms
• Sign changes of coefficients of half integral weight modular forms
• Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms