By Michel Courtieu

This booklet, now in its 2d version, is dedicated to the arithmetical idea of Siegel modular varieties and their L-functions. The imperative object are L-functions of classical Siegel modular varieties whose precise values are studied utilizing the Rankin-Selberg strategy and the motion of yes differential operators on modular varieties that have great arithmetical homes.

A new approach to p-adic interpolation of those serious values is gifted. an incredible classification of p-adic L-functions treated within the current ebook are p-adic L-functions of Siegel modular types having logarithmic progress. The given development of those p-adic L-functions makes use of detailed algebraic houses of the arithmetical Shimura differential operator.

The booklet may be very worthwhile for postgraduate scholars and for non-experts looking for a speedy method of a quickly constructing area of algebraic quantity thought. This re-creation is considerably revised to account for the recent reasons that experience emerged some time past 10 years of the most formulation for specific L-values when it comes to arithmetical idea of approximately holomorphic modular varieties.

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