Alexandros Groutides

Arithmetic aspects of Rankin-Selberg zeta-integrals

Zeta-integrals of Rankin type have been a cornerstone in the representation-theoretic approach toward the study of product L-functions. In this talk, I will motivate the construction of these objects for the Rankin-Selberg convolution of two modular forms. I will then introduce a natural general notion of integral input data at which the Rankin-Selberg zeta-integrals can be evaluated. Using this, I will present an integral version of Jacquet-Langland's GCD-result. If time permits, I will summarize key ingredients in our approach, which include a novel reinterpretation of these integrals, and works of A. Saha and E. Assing on values of local Whittaker new-vectors.