The Explicit Sato-Tate Conjecture and Densities Pertaining to Lehmer-Type Questions

Jeremy Rouse, Jesse Thorner

Let $f(z)={\sum }_{n=1}^{\infty }a(n)q^n\in S_k^{\text{new}}({\Gamma }_0(N))$ be a newform with squarefree level $N$ that does not have complex multiplication. For a prime $p$, define $θ_p\in…