On spectral large sieve inequalities

Abstract

The spectral large sieve inequality due to H. Iwaniec, that is an estimate for the mean square over a spectral interval of a linear form in the Fourier coefficients of Maass wave forms is reported by use of a formula of Y. Motohashi and the “hybrid” large sieve inequality. Then the result is generalized to the case, where the coefficients of the linear form may depend on the respective eigenvalue of the hyperbolic Laplacian, and also on a well-spaced set of points.