Topics in number theory / Jorge Morales

Format:

Book

Author/Creator:

Morales, Jorge, author., aut.

Series:

London Mathematical Society lecture note series ; 501.

London Mathematical Society lecture note series ; 501

Language:

English

Physical Description:

xiv, 370 pages ; 23 cm.

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"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."-- Provided by publisher.

Notes:

Includes index.

ISBN:

9781009720588

1009720589

OCLC:

1547895109