Name: Topics in Number Theory
Author: Jorge Morales (Author)
ISBN: 9781009720588

Topics in Number Theory book cover

Topics in Number Theory

Author(s): Jorge Morales (Author)

Publisher: Cambridge University Press
Publication Date: 9 April 2026
Language: English
Print length: 386 pages
ISBN-10: 1009720589
ISBN-13: 9781009720588

Book Description

Spanning elementary, algebraic, and analytic approaches, this book provides an introductory overview of essential themes in number theory. Designed for mathematics students, it progresses from undergraduate-accessible material requiring only basic abstract algebra to graduate-level topics demanding familiarity with algebra and complex analysis. The first part covers classical themes: congruences, quadratic reciprocity, partitions, cryptographic applications, and continued fractions with connections to quadratic Diophantine equations. The second part introduces key algebraic tools, including Noetherian and Dedekind rings, then develops the finiteness of class groups in number fields and the analytic class number formula. It also examines quadratic fields and binary quadratic forms, presenting reduction theory for both definite and indefinite cases. The final section focuses on analytic methods: L-series, primes in arithmetic progressions, and the Riemann zeta function. It addresses the Prime Number Theorem and explicit formulas of von Mangoldt and Riemann, equipping students with foundational knowledge across number theory's major branches.