Titlebook: Non-Archimedean L-Functions; of Siegel and Hilber Alexey A. Panchishkin Book 19911st edition Springer-Verlag Berlin Heidelberg 1991 11F.11R

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Siegel modular forms and the holomorphic projection operator, recall main properties of Siegel modular forms and of the action of the Hecke algebra on them, as well as the definitions of spinor zeta functions and standard zeta functions (§1), see also [An2], [An7]. Then in §2 we present some standard results on theta series with a Dirichlet character [An-M1],

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Non-Archimedean convolutions of Hilbert modular forms, their .-adic analogues; they correspond to certain automorphic forms on the group . = GL. × GL. over a totally real field . and have the form.where . are Hilbert automorphic forms of “holomorphic type” over ., and .(.), .(.) are their normalized Fourier coefficients (indexed by integral ideals . of

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Non-Archimedean analytic functions, measures and distributions,ucts.This construction provides a generalization of measures first introduced by Yu.I.Manin [Man4], B.Mazur and H.P.F.SwinnertonDyer [Maz-SD]. Our construction [Pa5], [Pa9] was already successfully used in several problems concerning the p-adic analytic interpolation of special values of Dirichlet s

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