Reference : Equidistribution of signs for modular eigenforms of half integral weight
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/11209
Equidistribution of signs for modular eigenforms of half integral weight
English
Inam, Ilker [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2013
Archiv der Mathematik [=ADM]
101
4
331--339
Yes
International
0003-889X
[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.
http://hdl.handle.net/10993/11209
10.1007/s00013-013-0566-4
http://dx.doi.org/10.1007/s00013-013-0566-4

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