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Lethbridge Number Theory and Combinatorics Seminar.
Lecturer(s): Peng-Jie Wong (University of Lethbridge)
Day/Date: Monday, Novermber 4, 2019
Time: 12 to 12:50 p.m.
Location: C630 University Hall
Topic:
Primes in Short Intervals.
Description:
Bertrand's postulate states that there is always a prime in the interval [x,2x] for any x > 1.
Applying the prime number theorem, one may further show that the number of primes in this interval is approximately the integral of 1/(log t) from x to 2x, if x is sufficiently large. There is a more difficult question concerning the distribution of primes p in short intervals when [x,2x] is replaced by [x,x+h] for some h < x and p is required to be congruent to a modulo q for some (a,q)=1. In this talk, we will discuss how short [x,x+h] can be. If time allows, we will sketch a proof of the Bombieri-Vinogradov theorem in short intervals, which answers such a question.
Other Information:
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
