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L-Functions: An Elementary Introduction by Davide Lombardo is a nonfiction available to read on EtoBox.

What is L-Functions: An Elementary Introduction about?

This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results. Designed to be elementary, it offers readers a clear pathway into the subject, starting from minimal background. It describes several important classes of L-functions — Riemann and Dedekind zeta functions, Dirichlet L-functions, and Hecke L-functions (for characters with finite image) — by showing how they are all special cases of the construction, due to Artin, of the L-function of a Galois representation. The analytic properties of abelian L-functions are presented in detail, including the full content of Tate's thesis, which establishes analytic continuation and functional equations via harmonic analysis. General Hecke L-functions are also discussed, using the modern perspective of idèles and adèles to connect their analytic theory with the representation-theoretic approach of Artin's L-functions. A distinguishing feature of this book is its accessibility: while largely avoiding arithmetic geometry, it provides introductions to both algebraic number theory and key aspects of representation theory. This approach

Who reads L-Functions: An Elementary Introduction?

Author

Davide Lombardo

Publisher

Springer Nature Switzerland AG

Published

2025

Language

EN

ISBN

9783031851445

Category

nonfiction

Subjects

Mathematics, Stem

Updated

2026-03-24