Abstract :
Let (X,μ) be a measurable topological space. Let S1,S2,… be a family of finite subsets of X. Suppose each x Si has a weight wix R+ assigned to it. We say {Si} is {wi}-distributed with respect to the measure μ if for any continuous function f on X, we have .
Let S(N,k) be the space of modular cusp forms over Γ0(N) of weight k and let be a basis which consists of Hecke eigenforms. Let ar(h) be the rth Fourier coefficient of h. Let xph be the eigenvalue of h relative to the normalized Hecke operator T′p. Let • be the Petersson norm on S(N,k). In this paper we will show that for any even integer k 3, is -distributed with respect to a polynomial times the Sato–Tate
