The first term identities for Eisenstein series (Q1267310)

The author studies the theory of Eisenstein series associated with maximal parabolic subgroups of \(Sp(2n)\) over a number field. These are functions of a single complex variable \(s\), and the author defines the ``largest'' singularity (measured by \(\text{Re}(s)\)). The subject of the investigation is the leading term considered as a linear functional. The Kudla-Rallis formula, itself an extension of the Siegel-Weil formula, can be considered as an identity between two such functionals. The author formulates a precise conjecture in a very general setting and proves this in certain cases. The last section is devoted to some local questions. The techniques used are mainly from the general theory of Eisenstein series, which the author develops in detail in this case.