Weighted spectral large sieve inequalities for Hecke congruence subgroups of SL2,ZiReport as inadecuate



 Weighted spectral large sieve inequalities for Hecke congruence subgroups of SL2,Zi


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We prove new bounds for weighted mean values of sums involving Fourier coefficients of cusp forms that are automorphic with respect to a Hecke congruence subgroup \Gamma =\Gamma 0q of the group SL2,Zi, and correspond to exceptional eigenvalues of the Laplace operator on the space L^2\Gamma\SL2,C-SU2. These results are, for certain applications, an effective substitute for the generalised Selberg eigenvalue conjecture. We give a proof of one such application, which is an upper bound for a sum of generalised Kloosterman sums of significance in the study of certain mean values of Hecke zeta-functions with groessencharakters. Our proofs make extensive use of Lokvenec-Guleskas generalisation of the Bruggeman-Motohashi summation formulae for PSL2,Zi\PSL2,C. We also employ a bound of Kim and Shahidi for the first eigenvalues of the relevant Laplace operators, and an `unweighted spectral large sieve inequality our proof of which is to appear separately.



Author: Nigel Watt

Source: https://archive.org/







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