[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.
Disciplines :
Mathematics
Author, co-author :
Inam, Ilker
Demirkol Özkaya, Zeynep
Tercan, Elif
Wiese, Gabor ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
yes
Language :
English
Title :
On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
Publication date :
2021
Journal title :
Turkish Journal of Mathematics
ISSN :
1300-0098
Publisher :
Scientific and Technical research Council of Turkey - TUBITAK/Turkiye Bilimsel ve Teknik Arastirma Kurumu, Turkey