The Prime Number Theorem
Sigurdur Helgason
Tue Jan 5, 12:30-02:00pm, 2-105
No enrollment limit, no advance sign up
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. This will be given in the lecture in full detail. The proof involves only standard Calculus except at the very end where Cauchy’s theorem in the complex
Contact: Sigurdur Helgason, 2-182, x3-3668, helgason@mit.edu
Sponsor: Mathematics
Latest update: 18-Dec-2009
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