ALGEBRAIC DIFFERENTIAL OPERATORS ON ARITHMETIC AUTOMORPHIC FORMS, MODULAR DISTRIBUTIONS, P -ADIC INTERPOLATION OF THEIR CRITICAL L VALUES VIA BGG MODULES AND HECKE ALGEBRAS
Résumé
The paper extends author’s method of modular distributions (2002, [75]) to arithmetic automorphic L functions on general classical groups. Main resultat gives a p-adic interpolation of their critical L values in the form of integrals of distributions constructed from a given eigen function of Hecke algebras by applying BGG modules, (see also preprints [78] and [79]. In particular, algebraic differential operators are described acting on auto-morphic forms ϕ on unitary groups U (n, n) over an imaginary quadratic field K = Q(√−D K ) ⊂ C. Applications are given to Shimura’s zeta functions L(s, f ) [90] attached special L-values L(s, ϕ) attached to ϕ. and normalized in accordance with Deligne’s Gamma factors rule [21]. An explicit description of Shimura’s Γ-factors is used..
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