Benford's Law for Coefficients of Newforms

Marie Jameson, Jesse Thorner, Lynnelle Ye

Let $f(z)={\sum }_{n=1}^{\infty }{\lambda }_f(n)e^{2\pi inz}\in S_k^{new}({\Gamma }_0(N))$ be a normalized Hecke eigenform of even weight $k\ge 2$ on ${\Gamma }_0(N)$ without complex multiplication. Let $\math…