Essays in Classical Number Theory

A comprehensive introduction to number theory demonstrating explicit problem-solving methods and exploring historical context.

Yoichi Motohashi (Author)

9781009504553, Cambridge University Press

Hardback, published 28 August 2025

702 pages
23.5 x 16 x 4.2 cm, 1.15 kg

Offering a comprehensive introduction to number theory, this is the ideal book both for those who want to learn the subject seriously and independently, or for those already working in number theory who want to deepen their expertise. Readers will be treated to a rich experience, developing the key theoretical ideas while explicitly solving arithmetic problems, with the historical background of analytic and algebraic number theory woven throughout. Topics include methods of solving binomial congruences, a clear account of the quantum factorization of integers, and methods of explicitly representing integers by quadratic forms over integers. In the later parts of the book, the author provides a thorough approach towards composition and genera of quadratic forms, as well as the essentials for detecting bounded gaps between prime numbers that occur infinitely often.

Preface
For readers
Table of theorems
1. Divisibility
2. Congruences
3. Characters
4. Quadratic forms
5. Distribution of prime numbers
Bibliography
Index.

Subject Areas: Number theory [PBH]