02541nam a2200385 i 4500991003632139707536m o d cr cn ||||a190327t2018 sz a ob 001 0 eng d9783030012885(electronic bk.)10.1007/978-3-030-01288-5doib14363239-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. MatematicaengAMS 22E50Li, Wen-Wei760810Zeta integrals, Schwartz spaces and local functional equations[e-book] /Wen-Wei LiCham, Switzerland :Springer,[2018?]©20181 online resource (viii, 141 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2228Includes bibliographical references and indexIntroduction ; Geometric background ; Analytic background ; Schwartz spaces and zeta integrals ; Convergence of some zeta integrals ; Prehomogeneous vector spaces ; The doubling method ; Speculation on the global integralsThis 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 difficultiesFunctional equationsFunctions, ZetaSchwartz spacesAn electronic book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-3-030-01288-5.b1436323903-03-2227-03-19991003632139707536Zeta integrals, Schwartz spaces and local functional equations1539991UNISALENTOle01327-03-19m@ -engsz 00