Introduction to Analytic Number Theory

Introduction to Analytic Number Theory
Arithmetical functions; distribution of primes; Dirichlet characters; Dirichlet's theorem; Gauss sums; primitive roots; Dirichlet L-functions; Riemann zeta-function; prime number theorem; partitions.
MATH
587
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesMath 352 or equivalent.
 TaughtFall Contact Department, Winter Contact Department, Spring Contact Department, Summer Contact Department
Course Outcomes

Learning Outcomes

Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 587 Wiki page.

Overview

  1. Arithmetic functions
  2. Elementary theorems on distribution of prime numbers
  3. Finite abelian groups and their characters
  4. Dirichlet series and Euler product
  5. The zeta function and the Dirichlet L-functions
  6. Partitions