LEADER 02766nam 2200529 450 001 9910495183803321 005 20230622200259.0 010 $a3-030-77263-2 024 7 $a10.1007/978-3-030-77263-5 035 $a(CKB)4100000011996610 035 $a(DE-He213)978-3-030-77263-5 035 $a(MiAaPQ)EBC6698062 035 $a(Au-PeEL)EBL6698062 035 $a(OCoLC)1263868884 035 $a(PPN)257353879 035 $a(EXLCZ)994100000011996610 100 $a20220428d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Eigenbook $eEigenvarieties, families of Galois representations, p-adic L-functions /$fJoe?l Bellai?che 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (XI, 316 p. 16 illus., 1 illus. in color.) 225 0 $aPathways in mathematics,$x2367-3451 311 $a3-030-77262-4 320 $aIncludes bibliographical references and index. 327 $a- Introduction -- Part I The ?Eigen? Construction -- Eigenalgebras -- Eigenvarieties -- Part II Modular Symbols and L-Functions -- Abstract Modular Symbols -- Classical Modular Symbols, Modular Forms, L-functions -- Rigid Analytic Modular Symbols and p-Adic L-functions -- Part III The Eigencurve and its p-Adic L-Functions -- The Eigencurve of Modular Symbols -- p-Adic L-Functions on the Eigencurve -- The Adjoint p-Adic L-Function and the Ramification Locus of the Eigencurve -- Solutions and Hints to Exercises. 330 $aThis book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution. 410 0$aPathways in Mathematics,$x2367-346X 606 $aNumber theory 606 $aTeoria de nombres$2thub 608 $aLlibres electrònics$2thub 615 0$aNumber theory. 615 7$aTeoria de nombres 676 $a512.7 700 $aBellai?che$b Joe?l$0851662 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495183803321 996 $aThe Eigenbook$91901592 997 $aUNINA