A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and Halász' Theorem

Abstract

In this note, we improve earlier results towards the Bruinier-Kohnen sign equidistribution conjecture for half-integral weight modular eigenforms in terms of natural density by using a consequence of Halász' Theorem. Moreover, applying a result of Serre we remove all unproved assumptions.

4 pages, main result made unconditional, minor changes due to referee's reports

References in corpus (3)

• On conjectures of Sato-Tate and Bruinier-Kohnen
• Equidistribution of Signs for Modular Eigenforms of Half Integral Weight
• Sign changes of Hecke eigenvalues

Cited by in corpus (8)

• Sign of Fourier coefficients of modular forms of half integral weight
• Equidistribution of signs for Hilbert modular forms of half-integral weight
• Sign Changes of Coefficients and Sums of Coefficients of L-Functions
• Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms
• On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
• Fast computation of half-integral weight modular forms
• Angular changes of complex Fourier coefficients of cusp forms
• A note on the extended Bruinier-Kohnen conjecture