On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen 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 half-integral 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 Bruinier-Kohnen Conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.11240
- arXiv:
- arXiv:2010.11240
- Bibcode:
- 2020arXiv201011240I
- Keywords:
-
- Mathematics - Number Theory;
- 11F30 (primary);
- 11F37;
- 11F25
- E-Print:
- v3: minor revision, might differ slightly from the published version