Year: 2014
Type: preprint
Abstract: We develop certain aspects of the theory of shifted multiple Dirichlet series and study their meromorphic continuations. These continuations are used to obtain explicit spectral first and second moments of Rankin-Selberg convolutions. One consequence is a Weyl type estimate for the Rankin-Selberg convolution of a holomorphic cusp form and a Maass form with spectral parameter $|t_j|\le T$, namely: $$ \left| L\left(\frac{1}{2}+ir, f\times u_j\right) \right| \ll_N T^{2/3+ε}, $$ uniformly, for $|r| \le T^{2/3}$, with the implied constant depending only on $f$ and the level $N$.
Source: arXiv (Cornell University)
Authors: Hoffstein, Jeff, Lee, Min
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1925187941