On the distribution of coefficients of halfintegral weight modular forms and the BruinierKohnen Conjecture
Abstract
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and halfintegral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the BruinierKohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.11240
 arXiv:
 arXiv:2010.11240
 Bibcode:
 2020arXiv201011240I
 Keywords:

 Mathematics  Number Theory;
 11F30 (primary);
 11F37;
 11F25
 EPrint:
 v3: minor revision, might differ slightly from the published version