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In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.
We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $SL_3(Zz)$ do not correlate with $q$-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky--Nelson, c
We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. Knopp generalized this t
Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of ordinary $p$-adic automorphic forms along a parabolic subgroup and show that they interpret all classical ordinary automorphic forms.
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also
For a hyperbolic surface embedded eigenvalues of the Laplace operator are unstable and tend to become resonances. A sufficient dissolving condition was identified by Phillips-Sarnak and is elegantly expressed in Fermis Golden Rule. We prove formulas