In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q 2−δ for any δ > 0, where N is the length of linear forms in the large sieve.
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL have been considered, in which analogous GL-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL. We give formulas for the...
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