Let tφ(n) denote the nth
normalized Fourier coefficient of a primitive holomorphic or
Maass cusp form φ for the full modular group.
Our goal is to study the high moments
Σn≤x
tφ(n)j and the
mean value
Σn≤x
tφ(nj)
over jth powers, through the (conjectural)
analytic properties of symmetric power
L-functions.