Fluctuations in the distribution of Hecke eigenvalues about the Sato-Tate measure

Neha Prabhu, Kaneenika Sinha

We study fluctuations in the distribution of families of $p$-th Fourier coefficients $a_f(p)$ of normalised holomorphic Hecke eigenforms $f$ of weight $k$ with respect to $SL_2(\ma…