Fouvry, EtienneGanguly, SatadalKowalski, EmmanuelMichel, Philippe2015-02-202015-02-202015-02-20201410.4171/Cmh/342https://infoscience.epfl.ch/handle/20.500.14299/111549WOS:000345957900009We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distribution of these arithmetic functions in two related residue classes. These results follow from asymptotic evaluations of the relevant moments, and depend crucially on results on the independence of monodromy groups related to products of Kloosterman sums.Divisor functionHecke eigenvaluesFourier coefficients of modular formsarithmetic progressionscentral limit theoremKloosterman sumsmonodromy groupSato-Tate equidistributiontext::journal::journal article::research article