Motohashi Y. Essays in Classical Number Theory 2025

Textbook in PDF format

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.
Contains non-trivial explicit examples throughout the volume, giving readers the confidence to solve numerically impressive problems
Precise historical information will teach readers the importance of knowing who did what, when, where, and how in academic research
A modestly theoretic approach throughout facilitates a self-contained volume suitable for independent study without the need for further reference sources