On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture

Reference : On the distribution of coefficients of half-integral weight modular forms and the Bru...


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/45707

Title :	On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
Language :	English
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) >]
Publication date :	2021
Journal title :	Turkish Journal of Mathematics
Publisher :	Scientific and Technical research Council of Turkey - TUBITAK/Turkiye Bilimsel ve Teknik Arastirma Kurumu
Volume :	45
Issue/season :	6
Pages :	2427-2440
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	1300-0098
Country :	Turkey
Abstract :	[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.
Permalink :	http://hdl.handle.net/10993/45707

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