MIT: Independent Activities Period: IAP

IAP 2013



The Prime Number Theorem

Sigurdur Helgason

Jan/08 Tue 01:00PM-02:30PM 2-147
Jan/10 Thu 01:00PM-02:30PM 2-147

Enrollment: Unlimited: No advance sign-up
Attendance: Participants must attend all sessions

The location of prime numbers is a central question in number theory. Around 1808, Legendre offered experimental evidence that the number P(x) of primes < x behaves like x/log x for large x. Tchebychev proved (1848) the partial result that the ratio of P(x) to x/log x for large x lies between 7/8 and 9/8. In 1896 Hadamard and de la Vallée Poussin independently proved the Prime Number Theorem that the limit of this ratio is exactly 1. Many distinguished mathematicians (particularly Norbert Wiener) have contributed to a simplification of the proof and now (by an important device by D.J. Newman and an exposition by D. Zagier) a very short and easy proof is available.                                                                                                                                  

These lectures follow Zagier's account of Newman's short proof on the prime number theorem. cf:    

1) D.J. Newman, Simple Analytic Proof of the Prime Number Theorem, Amer. Math. Monthly 87 (1980), 693-697.     

2) D. Zagier, Newman's short proof of the Prime Number Theorem, Amer. Math. Monthly 104 (1997), 705-708.

 

 

 

Sponsor(s): Mathematics
Contact: Sigurdur Helgason, 2-182, x3-3668, helgason@mit.edu