Inam, IlkerDemirkol Ozkaya, ZeynepTercan, ElifWiese, Gabor2025-05-102025-05-1020211300-00981303-614910.3906/mat-2105-402-s2.0-85121818794https://doi.org/10.3906/mat-2105-40https://hdl.handle.net/20.500.14720/8025Inam, Ilker/0000-0001-5765-1718; Tercan, Elif/0000-0001-6460-8400; Wiese, Gabor/0000-0001-5106-6737; Demirkol Ozkaya, Zeynep/0000-0003-1236-1797This 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.eninfo:eu-repo/semantics/openAccessModular Forms Of Half-Integer WeightFourier Coefficients Of Automorphic FormsRamanujan-Petersson ConjectureSato-Tate ConjectureDistribution Of CoefficientsSign ChangesArticle456Q2Q22427+WOS:000720562100001