03193nam 22006015 450 991030010980332120200707005954.03-030-01288-310.1007/978-3-030-01288-5(CKB)4100000007111134(DE-He213)978-3-030-01288-5(MiAaPQ)EBC6297259(PPN)232467439(EXLCZ)99410000000711113420181102d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierZeta Integrals, Schwartz Spaces and Local Functional Equations /by Wen-Wei Li1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (VIII, 141 p. 30 illus., 2 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;22283-030-01287-5 Introduction -- Geometric Background -- Analytic Background -- Schwartz Spaces and Zeta Integrals -- Convergence of Some Zeta Integrals -- Prehomogeneous Vector Spaces -- The Doubling Method -- Speculation on the Global Integrals.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.Lecture Notes in Mathematics,0075-8434 ;2228Topological groupsLie groupsHarmonic analysisNumber theoryTopological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Abstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Topological groups.Lie groups.Harmonic analysis.Number theory.Topological Groups, Lie Groups.Abstract Harmonic Analysis.Number Theory.515.75515.56Li Wen-Weiauthttp://id.loc.gov/vocabulary/relators/aut760810MiAaPQMiAaPQMiAaPQBOOK9910300109803321Zeta integrals, Schwartz spaces and local functional equations1539991UNINA