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On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture by Inam, Ilker; Özkaya, Zeynep Demirkol; Tercan, Elif; Wiese, Gabor is a scholarly article available to read on EtoBox.

What is On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture about?

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.

Author

Inam, Ilker; Özkaya, Zeynep Demirkol; Tercan, Elif; Wiese, Gabor

Published

2020

Language

EN