國立高雄大學圖資館 |

Language: English

Back

The EigenbookEigenvarieties, familie...

Bellaiche, Joel.

The EigenbookEigenvarieties, families of Galois representations, p-adic l-functions /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Eigenbookby Joel Bellaiche.
Reminder of title:	Eigenvarieties, families of Galois representations, p-adic l-functions /
Author:	Bellaiche, Joel.
Published:	Cham :Springer International Publishing :2021.
Description:	xi, 316 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Eigenfunctions.
Online resource:	https://doi.org/10.1007/978-3-030-77263-5
ISBN:	9783030772635

The EigenbookEigenvarieties, families of Galois representations, p-adic l-functions /
Bellaiche, Joel.

The EigenbookEigenvarieties, families of Galois representations, p-adic l-functions /[electronic resource] :by Joel Bellaiche. - Cham :Springer International Publishing :2021. - xi, 316 p. :ill., digital ;24 cm. - Pathways in mathematics,2367-346X. - Pathways in mathematics..

- 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.

This 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.

ISBN: 9783030772635

Standard No.: 10.1007/978-3-030-77263-5doiSubjects--Topical Terms:

243471
Eigenfunctions.

LC Class. No.: QA214 / .B45 2021

Dewey Class. No.: 512.32

The EigenbookEigenvarieties, families of Galois representations, p-adic l-functions /
LDR:02241nmm a2200337 a 4500 001 608148
003 DE-He213
005 20210811203737.0
006 m d
007 cr nn 008maaau
008 220119s2021 sz s 0 eng d
020 $a 9783030772635 $q (electronic bk.)
020 $a 9783030772628 $q (paper)
024 7 $a 10.1007/978-3-030-77263-5 $2 doi
035 $a 978-3-030-77263-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA214 $b .B45 2021
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.32 $2 23
090 $a QA214 $b .B435 2021
100 1 $a Bellaiche, Joel. $3 905472
245 1 4 $a The Eigenbook $h [electronic resource] : $b Eigenvarieties, families of Galois representations, p-adic l-functions / $c by Joel Bellaiche.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2021.
300 $a xi, 316 p. : $b ill., digital ; $c 24 cm.
490 1 $a Pathways in mathematics, $x 2367-346X
505 0 $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.
520 $a This 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.
650 0 $a Eigenfunctions. $3 243471
650 1 4 $a Number Theory. $3 274059
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Pathways in mathematics. $3 750319
856 4 0 $u https://doi.org/10.1007/978-3-030-77263-5
950 $a Mathematics and Statistics (SpringerNature-11649)