Benford's law for coefficients of newforms (Q2789377)

Let \(\mathbb{P}\) denote the set of all primes, and let \(f(z)=\sum_{n=1}^\infty\lambda_f(n)e^{2\pi i n z}\in S_k^{\text{new}}(\Gamma_0(N))\) be a newform (a holomorphic cuspidal normalized Hecke eigenform) of even weight \(k\geq 2\) on \(\Gamma_0(N)\) without complex multiplication. In the paper under review, the authors utilize the now proven Sato-Tate conjecture to prove that the sequence \((\lambda_f(p))_{p\in\mathbb{P}}\) is not Benford, however, it is logarithmically Benford.