On conjectures of Sato-Tate and Bruinier-Kohnen

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.

26 pages; to appear in The Ramanujan Journal

References in corpus (1)

• Equidistribution of Signs for Modular Eigenforms of Half Integral Weight

Cited by in corpus (6)

• A Short Note on the Bruinier-Kohnen Sign Equidistribution Conjecture and Halász' Theorem
• Sign Changes of Coefficients and Sums of Coefficients of L-Functions
• Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms
• Angular changes of complex Fourier coefficients of cusp forms
• A note on the extended Bruinier-Kohnen conjecture
• On the coefficients of symmetric power $L$-functions