THE THEORY OF NUMBERS
AN INTRODUCTION

Developed for a first course in number theory, this text features the use of algebraic methods for studying arithmetic functions. Unlike many others texts, it emphasizes the algebraic structure of the set of functions under Dirichlet convolutions.

Among the topic covered are fundamental concepts, including divisibility ant the Euclidean algorithm, arithmetic functions, congruences and residues, summatory functions, continued fractions, Farey sequences, the Pell equations, and the Erdös-Selberg proof of the Prime Number Theorem. The text also introduces algebraic and geometric number theory - the former by studying Gaussian and Jacobian integers, the latter through geometric methods in proving the Quadratic Reciprocity Law and in proofs of certain asymptotic formulas for summatory functions.