Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2016

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

Résumé

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
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Dates et versions

hal-01329432 , version 1 (09-06-2016)
hal-01329432 , version 2 (03-10-2016)

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Alexei Panchishkin. Graded structures and differential operators on nearly holomorphic and quasimodular forms on classical groups. 2016. ⟨hal-01329432v1⟩
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