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Graduate Seminar

Zilin Jiang
Carnegie Mellon University
Title: Races beyond Riemann hypothesis

Abstract: This is just an ordinary day in the world of primes and a race is about to start. Contestant 1 and 3 are ready to dash out. After the starter's pistol sounds, you gradually realize the unusual rule of the game. "Darn! It is the mod 4 race between primes." On the p'th second, contestant 1 gets to advance one inch if p is a prime of the form 4n+1 and contestant 3 gets to advance 1 inch if p is of the form 4n+3. Quickly your enthusiasm fades away, but something extraordinary is unfolding in front of you. "This cannot be real!" For the first 6 hours, contestant 3 is always leading. You start to wonder if contestant 1 will ever take the lead...

In this talk, we will get to see the full story of the mod 4 race, among many other races in the world of primes, featuring Littlewood, Tchebychev and Gauss. As part of the story assumes the Riemann hypothesis, audience's imagination is fully encouraged.

Date: Tuesday, April 19, 2016
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/v4OMOnmW_0g