Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore a novel mathematical approach for determining holomorphy regions of Eisenstein series through the Franke filtration in this workshop lecture. Learn about the fundamental concepts of automorphic forms, Eisenstein series, and the Franke filtration, which creates a finite descending filtration of automorphic form spaces on adelic points of reductive groups over number fields. Discover how the key insight that residues from poles in Eisenstein series contribute to deeper filtration quotients leads to a new method for analyzing degenerate Eisenstein series. Examine the practical application of this method specifically to Eisenstein series on the general linear group. Gain comprehensive understanding of the theoretical framework including cuspidal support, main values of derivatives, and the relationship between poles and filtration depth. This presentation serves as both an introduction to advanced topics in automorphic forms and a detailed exposition of cutting-edge research in determining holomorphy regions, making it valuable for researchers working in number theory, representation theory, and related areas of mathematics.
