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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