Supplement to a Shimura's theorem on Eisenstein series
Shoyu Nagaoka
TL;DR
This paper refines Shimura's original results on the analytic properties and residue formulas of non-holomorphic Siegel Eisenstein series, extending the understanding of their behavior.
Contribution
It provides a refined version of Shimura's theorem for various types of Eisenstein series, enhancing the existing theoretical framework.
Findings
Refined residue formulas for Eisenstein series
Extended results to multiple types of Eisenstein series
Improved understanding of their analytic properties
Abstract
Shimura studied the analytic properties of the non-holomorphic Siegel Eisenstein series and derived a residue formula. Herein, we provide a refinement of his result for several types of Eisenstein series.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Analytic Number Theory Research