Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2105-40
Keywords
Modular forms of half-integer weight, Fourier coefficients of automorphic forms, Ramanujan-Petersson conjecture, Sato-Tate conjecture, distribution of coefficients, sign changes
First Page
2427
Last Page
2440
Recommended Citation
İNAM, İ, ÖZKAYA, Z. D, TERCAN, E, & WIESE, G (2021). On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture. Turkish Journal of Mathematics 45 (6): 2427-2440. https://doi.org/10.3906/mat-2105-40
