LEADER 03193nam 22006015 450 001 9910300109803321 005 20200707005954.0 010 $a3-030-01288-3 024 7 $a10.1007/978-3-030-01288-5 035 $a(CKB)4100000007111134 035 $a(DE-He213)978-3-030-01288-5 035 $a(MiAaPQ)EBC6297259 035 $a(PPN)232467439 035 $a(EXLCZ)994100000007111134 100 $a20181102d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aZeta Integrals, Schwartz Spaces and Local Functional Equations /$fby Wen-Wei Li 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (VIII, 141 p. 30 illus., 2 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2228 311 $a3-030-01287-5 327 $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. 330 $aThis book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2228 606 $aTopological groups 606 $aLie groups 606 $aHarmonic analysis 606 $aNumber theory 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aTopological groups. 615 0$aLie groups. 615 0$aHarmonic analysis. 615 0$aNumber theory. 615 14$aTopological Groups, Lie Groups. 615 24$aAbstract Harmonic Analysis. 615 24$aNumber Theory. 676 $a515.75 676 $a515.56 700 $aLi$b Wen-Wei$4aut$4http://id.loc.gov/vocabulary/relators/aut$0760810 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300109803321 996 $aZeta integrals, Schwartz spaces and local functional equations$91539991 997 $aUNINA