# Weighted spectral large sieve inequalities for Hecke congruence subgroups of \$SL(2,\mathbb{Z}[i])\$

```@inproceedings{Watt2013WeightedSL,
title={Weighted spectral large sieve inequalities for Hecke congruence subgroups of \\$SL(2,\mathbb\{Z\}[i])\\$},
author={Nigel Watt},
year={2013}
}```
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_0(q) of the group SL(2,Z[i]), and correspond to exceptional eigenvalues of the Laplace operator on the space L^2(\Gamma\SL(2,C)/SU(2)). 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… CONTINUE READING
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