Growth of Fourier coefficients of vector-valued automorphic forms

Dimension formulae for vector valued automorphic forms

More general results, including arbitrary Fuchsian groups, can be found in the paper [Bo2] of Borcherds, Sect. 7. Most of them have been proved by the Selberg trace formula, see [Iv] and also [Fi]. The Selberg trace formula in its standard form causes the restriction that the weight is > 2. Borcherds mentions that “with a bit more care this also works for weight 2”. As we mentioned, this bit mo...

FOURIER COEFFICIENTS OF GLpNq AUTOMORPHIC FORMS IN ARITHMETIC PROGRESSIONS

Abstract. We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GLpNq Maass cusp forms for all N > 2, satisfy a central limit theorem in a suitable range, generalizing the case N “ 2 treated by É. Fouvry, S. Ganguly, E. Kowalski and P. Michel in [4]. Such universal Gaussian behaviour relies on a deep e...

On the Fourier Coefficients of Automorphic Forms on Gl2

Given E/F a quadratic extension of number fields and a cuspidal representation π of GL2(AE), we give a full description of the fibers of the Asai transfer of π. We then determine the extent to which the Hecke eigenvalues of all the Hecke operators indexed by integral ideals in F determine the representation π.

Fourier Coefficients of Gl(n) Automorphic Forms in Arithmetic Progressions

Fourier Coefficients of Modular Forms

These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.