Ned Carmichael

Sums of Hecke eigenvalues

Motivated by the Dirichlet divisor problem, which asks for the best possible error term in the classical asymptotic formula for sums of the divisor function, we consider sums of Hecke eigenvalues attached to holomorphic cusp forms. We discuss some recent results, which reveal transitions in the average size of these sums as the length of the sums varies relative to the weight of the forms.