Scientific and Technical research Council of Turkey - TUBITAK/Turkiye Bilimsel ve Teknik Arastirma Kurumu

45

6

2427-2440

Yes (verified by ORBi^{lu})

International

1300-0098

Turkey

[en] 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.