LEADER 02541nam a2200385 i 4500 001 991003632139707536 006 m o d 007 cr cn ||||a 008 190327t2018 sz a ob 001 0 eng d 020 $a9783030012885$q(electronic bk.) 024 7 $a10.1007/978-3-030-01288-5$2doi 035 $ab14363239-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 084 $aAMS 22E50 100 1 $aLi, Wen-Wei$0760810 245 10$aZeta integrals, Schwartz spaces and local functional equations$h[e-book] /$cWen-Wei Li 264 1$aCham, Switzerland :$bSpringer,$c[2018?] 264 4$cİ2018 300 $a1 online resource (viii, 141 pages) :$billustrations (some color) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2228 504 $aIncludes bibliographical references and index 505 0 $aIntroduction ; 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 520 $aThis book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties 650 0$aFunctional equations 650 0$aFunctions, Zeta 650 0$aSchwartz spaces 856 40$zAn electronic book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-3-030-01288-5 907 $a.b14363239$b03-03-22$c27-03-19 912 $a991003632139707536 996 $aZeta integrals, Schwartz spaces and local functional equations$91539991 997 $aUNISALENTO 998 $ale013$b27-03-19$cm$d@ $e-$feng$gsz $h0$i0