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The EigenbookEigenvarieties, familie...

Bellaiche, Joel.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Eigenbookby Joel Bellaiche.
其他題名:	Eigenvarieties, families of Galois representations, p-adic l-functions /
作者:	Bellaiche, Joel.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xi, 316 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Eigenfunctions.
電子資源:	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 /
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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.
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