Analytic Number Theory

(1-3 Credit Hours) · Undergraduate

The aim of this course is to study the prime numbers using the famous Riemann function. In particular, we will study the connection between the primes and the zeros of the function. We will state the Riemann hypothesis, perhaps the most famous unsolved problem in mathematics, and examine its implication for the distribution of primes. We will prove the prime number theorem, which states that the number of primes less than X is asymptotic to X/ logX.