Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups

Alexei Panchishkin (1)

1 IF - Institut Fourier

We wish to use graded structures [KrVu87], [Vu01] on dffierential operators and quasimodular forms on classical groups and show that these structures provide a tool to construct p-adic measures and p-adic L-functions on the corresponding non-archimedean weight spaces. An approach to constructions of automorphic L-functions on uni-tary groups and their p-adic avatars is presented. For an algebraic group G over a number eld K these L functions are certain Euler products L(s, π, r, χ). In particular, our constructions cover the L-functions in [Shi00] via the doubling method of Piatetski-Shapiro and Rallis. A p-adic analogue of L(s, π, r, χ) is a p-adic analytic function L p (s, π, r, χ) of p-adic arguments s ∈ Z p , χ mod p r Presented in a talk for the INTERNATIONAL SCIENTIFIC CONFERENCE "GRADED STRUCTURES IN ALGEBRA AND THEIR APPLICATIONS" dedicated to the memory of Prof. Marc Krasner on Friday, September 23, 2016, International University Centre (IUC), Dubrovnik, Croatia.

Mots clés: Fourier coeffcients.; graded structures; automorphic forms; classical groups; non-archimedean weight spaces; quasi- modular forms; p-adic L-functions; differential operators

Domaines: Théorie des nombres [math.NT]

Alexei Panchishkin. Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups. Sarajevo Journals of Mathematics, 2016, 12 (25). ⟨hal-01329432v2⟩