On conjectures of Sato-Tate and Bruinier-Kohnen

Reference : On conjectures of Sato-Tate and Bruinier-Kohnen


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/11503

Title :	On conjectures of Sato-Tate and Bruinier-Kohnen
Language :	English
Author, co-author :	Arias De Reyna Dominguez, Sara [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
	Inam, Ilker [> >]
	Wiese, Gabor [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Publication date :	2015
Journal title :	The Ramanujan Journal
Volume :	36
Issue/season :	3
Pages :	455-481
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
e-ISSN :	1572-9303
Keywords :	[en] Mathematics - Number Theory ; 11F37 (primary) ; 11F30 ; 11F80 ; 11F11
Abstract :	[en] This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on a conjecture of Bruinier and Kohnen in three ways: the CM-case is included; under the assumption of the same error term as in previous work one obtains the result in terms of natural density instead of Dedekind-Dirichlet density; the latter type of density can already be achieved by an error term like in the prime number theorem. (3) It also provides a complete proof of Sato-Tate equidistribution for CM modular forms with an error term similar to that in the prime number theorem.
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/11503
DOI :	10.1007/s11139-013-9547-2

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