Generalized Kloosterman sums and the Fourier coefficients of cusp forms

Abstract

Certain generalized Kloosterman sums connected with congruence subgroups of the modular group and suitably restricted multiplier systems of half-integral degree are studied. Then a Fourier coefficient estimate is obtained for cusp forms of half-integral degree on congruence subgroups of the modular group and the Hecke groups G ( 2 ) G(\sqrt 2 ) and G ( 3 ) G(\sqrt 3 ) .