L-Functions: (Record no. 8157)

MARC details
000 -LEADER
fixed length control field 02332 a2200181 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20260327150608.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 260327b |||||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9783031851445
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.7
Item number LomL
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name Lombardo, Davide
245 ## - TITLE STATEMENT
Title L-Functions:
Remainder of title An Elementary Introduction/
Statement of responsibility, etc Davide Lombardo
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Switzerland:
Name of publisher Springer,
Year of publication ©2025.
300 ## - PHYSICAL DESCRIPTION
Number of Pages xiv, 261p.
490 ## - SERIES STATEMENT
Series statement Unitext 171
520 ## - SUMMARY, ETC.
Summary, etc 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 ensures that the material is accessible to both beginning graduate students and advanced undergraduates. Applications play a central role throughout, highlighting how L-functions underpin significant results in number theory. The book provides complete proofs of the prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, Chebotarev's density theorem, and the analytic class number formula, demonstrating the power of the theory in solving classical problems. It serves as an ideal introduction for advanced undergraduates and beginning graduate students and can also be a useful reference for preparing a course on the subject.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Number Theory
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Books
Holdings
Withdrawn status Lost status Damaged status Collection code Home library Current library Shelving location Date acquired Purchase Price Bill number Full call number Accession Number Print Price Bill Date/Price effective from Koha item type
      Mathematics Indian Institute of Technology Tirupati Indian Institute of Technology Tirupati General Stacks 26/03/2026 3283.34 IN36763/25-26 512.7 LomL (12518) 12518 5969.71 26/03/2026 Books