Reference : On the distribution of coefficients of half-integral weight modular forms and the Bru...
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45707
On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
English
Inam, Ilker []
Demirkol Özkaya, Zeynep []
Tercan, Elif []
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
2020
No
[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.
http://hdl.handle.net/10993/45707
https://arxiv.org/abs/2010.11240

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