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2016 | OriginalPaper | Chapter

Germ Expansions for Real Groups

Author : James Arthur

Published in: Families of Automorphic Forms and the Trace Formula

Publisher: Springer International Publishing

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Abstract

We shall introduce an archimedean analogue of the theory of p-adic Shalika germs. These are the objects for p-adic groups that govern the singularities of invariant orbital integrals. More generally, we shall formulate an archimedean theory of germs for weighted orbital integrals. In the process we shall be led to some interesting questions on a general class of asymptotic expansions. Weighted orbital integrals are the parabolic terms on the geometric side of the trace formula. An understanding of their singularities is important for the comparison of trace formulas. It might also play a role in the deeper spectral analysis of a single trace formula.

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next chapter Slopes of Modular Forms

I thank Waldspurger for pointing this version of the expansion out to me. My original formulation [A3, Proposition 9.1] was less elegant.

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Title: Germ Expansions for Real Groups
Author: James Arthur
Publisher: Springer International Publishing
Book: Families of Automorphic Forms and the Trace Formula
Print ISBN: 978-3-319-41422-5

Electronic ISBN: 978-3-319-41424-9

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-41424-9_1

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