Student Analysis Date:  Thursday, January 24, 2013 Location:  3096 East Hall (5:10 PM to 6:00 PM) Title:  The Prime Number Theorem Abstract:   The prime number theorem (PNT) is the most important result of analytic number theory. The PNT states that the growth of the prime counting function is asymptotic to the logarithmic integral function li(x). A concrete program to attack PNT was first outlined by Riemann in his amazingly influential 1859 paper "On the number of primes less than a given magnitude". The proof was finally completed independently by Hadamard and de la Valle-Poussin in 1896. Though we now have many different proofs of the prime number theorem, the original proof stands out for its beauty and transparency. The proof is notable for combining many different techniques from both real and complex analysis. I will give a detailed outline of the proof and try to explain what I think are the key ideas. Speaker:  Matt Jacobs Institution:  University of Michigan Event Organizer:   Purvi Gupta      Edit this event (login required). Add new event (login required). For access requests and instructions, contact math-webmaster@umich.edu Back to previous page Back to UM Math seminars/events page.