Zeta Integrals, Schwartz Spaces and Local Functional Equations
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Beschreibung
This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions.
Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions.
Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
Offers a clearly written, timely addition to the literature Provides concrete results complementing the more philosophical ideas of Sakellaridis Reviews many recent results and reformulates them in a more natural form
Autor*in
Wen-Wei Li
Themen in »Zeta Integrals, Schwartz Spaces and Local Functional Equations«
Distinguished Representation Local Functional Equation Poisson Formula Schwartz Space Zeta Integral
Stimmen zu »Zeta Integrals, Schwartz Spaces and Local Functional Equations«
“The book is carefully written; it enables the reader to navigate through highly technical material. The overview of classical results and thorough presentation of the background material make the book accessible to a wider audience of mathematicians.” (Dubravka Ban, Mathematical Reviews, August, 2019)
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