On the estimation of eigenvalues of Hecke operators (Q1073071)

This is the collection of results concerning lower estimates of the first eigenvalue of an automorphic Laplacian and Fourier coefficients of a cusp form. As an example one can see the following interesting result \[ \sum_{c\leq x}(1/c)\quad S(n,m;c)=\Omega (\exp (c_ 0 \log x/\log \log x)) \] for some \(c_ 0>0\) where S is the Kloosterman sum, \[ S(n,m;c)=\sum_{ad\equiv 1 (mod c)}\exp (2\pi i(nd+ma)/c). \]