The Gross--Prasad conjecture predicts a relation between periods of automorphic forms on the product SO(n) x SO(n+1), for any n, and square roots of central L-values. Focussing on the cases n = 3 and n = 4, we study these Gross--Prasad periods for cohomological automorphic forms, showing that in nice situations they can be expressed as algebraic multiples of explicit transcendental periods, and their algebraic parts vary analytically in p-adic families. I will also discuss the "degenerate case" of non-cuspidal automorphic representations, and how it links with the results on Euler systems which will be presented in Sarah Zerbes' talk (tomorrow Wednesday, HS5, at 16h15).
Gross-Prasad periods and p-adic interpolation
06.12.2022 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: