Introduction to Analytic Number Theory

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions.

Pseudo Differential Operators & Markov Processes, Volume I

Volume 1: Fourier Analysis and Semigroups. Handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.