Piatetski-Shapiro primes and exponential sums

Friday, October 25, 2013 - 4:00pm
MSB 312
Zhenyu Guo (University of Missouri, Columbia)

In this talk I state and prove the Piatetski-Shapiro prime number theorem, which concerns primes of the form p=[n^c], where n varies over the natural numbers and c is a real number exceeding one. Using bounds on exponential sums, I will show how one can obtain an asymptotic formula for such primes if c is not too large. I will also describe some other results on exponential sums.