Article (Scientific journals)
Equidistribution of signs for modular eigenforms of half integral weight
Inam, Ilker; Wiese, Gabor
2013In Archiv der Mathematik, 101 (4), p. 331--339
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Abstract :
[en] Let f be a cusp form of weight k+1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We prove this conjecture for certain subfamilies of coefficients that are accessible via the Shimura lift by using the Sato-Tate equidistribution theorem for integral weight modular forms. Firstly, an unconditional proof is given for the family {a(tp^2)}_p where t is a squarefree number and p runs through the primes. In this case, the result is in terms of natural density. To prove it for the family {a(tn^2)}_n where t is a squarefree number and n runs through all natural numbers, we assume the existence of a suitable error term for the convergence of the Sato-Tate distribution, which is weaker than one conjectured by Akiyama and Tanigawa. In this case, the results are in terms of Dedekind-Dirichlet density.
Disciplines :
Mathematics
Author, co-author :
Inam, Ilker
Wiese, Gabor  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Equidistribution of signs for modular eigenforms of half integral weight
Publication date :
2013
Journal title :
Archiv der Mathematik
ISSN :
0003-889X
Volume :
101
Issue :
4
Pages :
331--339
Peer reviewed :
Peer reviewed
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since 18 November 2013

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