By Michel Courtieu

This publication, now in its 2d version, is dedicated to the arithmetical concept of Siegel modular kinds and their L-functions. The imperative object are L-functions of classical Siegel modular kinds whose detailed values are studied utilizing the Rankin-Selberg process and the motion of definite differential operators on modular varieties that have great arithmetical homes.

A new approach to p-adic interpolation of those severe values is gifted. a tremendous category of p-adic L-functions treated within the current publication are p-adic L-functions of Siegel modular types having logarithmic progress. The given building of those p-adic L-functions makes use of special algebraic homes of the arithmetical Shimura differential operator.

The publication can be very worthy for postgraduate scholars and for non-experts looking for a quickly method of a speedily constructing area of algebraic quantity conception. This re-creation is considerably revised to account for the hot causes that experience emerged some time past 10 years of the most formulation for specified L-values when it comes to arithmetical idea of approximately holomorphic modular kinds.

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