The Eigenbook: Eigenvarieties, families of Galois representations, p-adic L-functions

This book is about p-adic modular forms, the eigencurve that parameterizes them, and the p-adic L-functions that can be associated to them, which are of fundamental importance in number theory. It provides a solid introduction for graduate students and newcomers, and offers foundational definitions and theorems with complete and self-contained proofs for experts.

Format: Hardback
Length: 316 pages
Publication date: 13 August 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the intricate world of p-adic modular forms, exploring their mathematical structures, eigencurves, and associated p-adic L-functions. These theories hold immense significance in number theory, with profound generalizations to automorphic forms for higher-rank groups. Designed for both graduate students and newcomers to the field, this book offers a solid foundation for understanding this highly active and rapidly evolving area of research. With its clear and concise explanations, accompanied by comprehensive proofs, it serves as a valuable resource for experts seeking to consolidate foundational definitions and theorems. Written in an engaging and accessible style, the book includes a wealth of exercises and their solutions, fostering a deeper understanding of the subject matter. Whether you are a student embarking on a journey into the world of number theory or an experienced researcher seeking to expand your knowledge, this book is an indispensable guide.

Weight: 658g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030772628
Edition number: 1st ed. 2021