Roelof W. Bruggeman

Fourier coefficients of cusp forms

AbstractLet ψ1,ψ2,ψ3,... be an orthonormal basis of the space of cusp forms of weight zero for the full modular group. Let be the Fourier series expansion. The following theorem is proved: Let σ∈(1/4, 1/2); letf be a holomorphic function on the strip |Res|≦σ, satisfyingf(−s)=f(s) and

A new approach to the spectral theory of the fourth moment of the Riemann zeta-function

f(s) = \mathcal{O}(|\tfrac{1}{4} - s^2 |^{ - 2} |cos \pi s|^{ - 1} )

Holomorphic automorphic forms and cohomology

on this strip; letm andn be non-zero integers, then

Period Functions for Maass Wave Forms and Cohomology

\sum\limits_{j = 1}^\infty {f(s_j )\bar \gamma _{jm} \gamma _{jn} }

Dedekind sums and Fourier coefficients of modular forms

converges and is equal to