Determination of ${\bf GL}(2)$ Maass forms from twists in the level aspect
Volume 189 / 2019
Acta Arithmetica 189 (2019), 165-178
MSC: 11F67, 11F11, 11F66.
DOI: 10.4064/aa180314-2-9
Published online: 10 May 2019
Abstract
We address the problem of determining a ${\bf GL}(2)$ Maass cusp form (of weight zero) from the central values of the Rankin–Selberg $L$-functions $L(1/2,f\otimes u_j)$ for infinitely many primes $p$ and all the normalised Maass cusp forms $u_j$ which are newforms for $\varGamma_0(p)$. This generalises Luo’s result on determining holomorphic cuspidal newforms.
