Publication: On conjectures of Sato-Tate and Bruinier-Kohnen
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Inam, Ilker
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Arias, Reyna de Sara
Wiese, Gabor
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Springer
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Abstract
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.
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Mathematics, Half-integral weight modular forms, Shimura lift, Sato-Tate equidistribution, Fourier coefficients of modular forms, Density of sets of primes, Half-integral weight, Modular-forms, Fourier coefficients, Prime-numbers, Values
Citation
Arias-de-Reyna, S. vd. (2015). "On conjectures of Sato-Tate and Bruinier-Kohnen". Ramanujan Journal, 36(3), 455-481.