Zeta functions and the trace formula
Prehomogeneous vector spaces provide a framework for the method of analytic continuation of the zeta integrals due to Hecke, Iwasawa and Tate. In this article, describes instances where convergence can only be achieved by truncation, for the purpose of special values of such zeta integrals appear in the Arthur-Selberg trace formula and their study is relevant in connection with recent ideas in the Langlands programs. A very clear explanation is written through concrete examples of five prehomogeneous vector spaces. Especially the explicit determination of the principal part of zeta distributions and its application are very interesting. For the entire collection see [Zbl 1416.60012].
scientific article; zbMATH DE number 7219051
scientific article