THE EFFECTIVE SATO-TATE CONJECTURE AND DENSITIES PERTAINING TO LEHMER-TYPE QUESTIONS

Abstract

We prove a completely explicit version of the Sato-Tate Conjecture for newforms f(z) on Gamma_0(N) with squarefree level. This result assumes that the symmetric power L-functions of f(z) are automorphic and satisfy the Generalized Riemann Hypothesis. We use this result to compute the density of positive integers n for which the n-th Fourier coefficient of f(z) is nonzero.