K. Holm

Spectral $L^2$-bounds on Eisenstein series and Diophantine properties of quadratic forms

We give $L^2$-bounds with respect to the height of the spectral parameter for Epstein zeta functions $\mathrm{Z}_Q(s)$ and non-holomorphic Eisenstein series $E_{\mathfrak{c}}(s,z)$ attached to the Hecke congruence subgroup $\Gamma_0 (p)$ of prime level $p$. Our bounds are completely explicit in the level and, additiona...