On inner products involving holomorphic cusp forms and Maass forms

Author:

Eeva SUVITIE

AMS Classification:

11F12

Keywords:

additive divisor problem and its analogues for Fourier coefficients of cusp forms, holomorphic cusp forms Maass wave forms, Petersson inner product, sums over short intervals

Abstract:

Let c_{j}=(u_{j}(z),y^{k}|F(z)|^{2}) stand for the Petersson inner product, involving a Maass wave form u_{j}(z) and a holomorphic cusp form F(z) of weight k. The proof of following estimation over a spectral short interval is outlined: For all K\geq 1 and \varepsilon>0, \sum_{K\leq\kappa_{j}\leq K+K^{\frac{1}{3}}}|c_{j}|^{2}\exp(\pi\kappa_{j})\ll K^{2k-\frac{2}{3}+\varepsilon}, where \kappa_{j} is the spectral parameter attached to the form u_{j}.

Download paper:

suvitie-08.pdf

Vol. 3 (11), 2008