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.

Yoichi Motohashi is a mathematician and foreign member of the Finnish Academy of Science and Letters. He received his D.Sc from the University of Tokyo. He is the author of Lectures on sieve methods and prime number theory (1983), Spectral theory of the Riemann zeta-function (Cambridge, 1997) and the editor of Analytic Number Theory (Cambridge, 1997).