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See detailOn the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
Inam, Ilker; Demirkol Özkaya, Zeynep; Tercan, Elif et al

in Turkish Journal of Mathematics (2021), 45(6), 2427-2440

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 ... [more ▼]

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. [less ▲]

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