03061nam 2200589 450 99646653860331620220821135340.03-540-38854-010.1007/BFb0082111(CKB)1000000000437501(SSID)ssj0000321393(PQKBManifestationID)12116012(PQKBTitleCode)TC0000321393(PQKBWorkID)10279842(PQKB)11320269(DE-He213)978-3-540-38854-8(MiAaPQ)EBC5595418(Au-PeEL)EBL5595418(OCoLC)1076233237(MiAaPQ)EBC6812111(Au-PeEL)EBL6812111(OCoLC)1287129415(PPN)155173227(EXLCZ)99100000000043750120220821d1988 uy 0engurnn|008mamaatxtccrArithmetic of p-adic modular forms /Fernando Q. Gouvêa1st ed. 1988.Berlin, Heidelberg :Springer-Verlag,[1988]©19881 online resource (X, 122 p.) Lecture Notes in Mathematics ;1304Bibliographic Level Mode of Issuance: Monograph3-540-18946-7 Contents: p-adic Modular Forms: Level Structures and Trivializations. p-adic Modular Forms with Growth Conditions. Generalized p-adic Modular Functions -- Hecke and U Operators: Hecke Operators. The Frobenius Operator. The U Operator. Appendix: Hida's Theory of the Ordinary Part -- Galois Representations: Duality Theorems. Families of Modular Forms. Changing the Level. Deformations of Residual Eigenforms. Deformations of Galois Representations. The Modular Deformation Space. Further Questions.The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.Lecture notes in mathematics ;1304.Forms, ModularForms, Modular.512.73Gouvêa Fernando Q(Fernando Quadros),382239MiAaPQMiAaPQMiAaPQBOOK996466538603316Arithmetic of p-adic modular forms381139UNISA