SIMUW 2007: What is Riemann's Hypothesis?

William Stein

"In the opinion of many mathematicians, the Riemann hypothesis, and its extension to general classes of L-functions, is probably today the most important open problem in pure mathematics." -- Fields Medalist Enrique Bombieri

Our mission is to explain -- in elementary terms -- the Riemann Hypothesis.

Notes A [PDF] (10MB) of some rough notes by Barry Mazur and me on the Riemann Hypothesis.
SAGE The SIMUW SAGE Notebook          SAGE Homepage          Documentation
Book/Course Some of the book for this course will be very relevant.
Documents Riemann's original manuscript, Riemann's paper, Riemann's paper in English,
Riesel-Gohl, Zagier's paper, Clay Math Inst problem description Prime Number Races Leech's paper


Monday, June 25Introduction to SAGE
Tuesday, June 26State Riemann Hypothesis 1; integer factorization; enumeration of primes; Mersenne primes
Thursday, June 28Frequency of prime gaps; Square root approximation, Li(x) and Riemann Hypothesis 2; multiplicative parity
Friday, June 29Calculus; Complex numbers; Blip functions;
Monday, July 2 Staircase of primes; distorted staircase and Phi(t); Fourier theory I
Tuesday, July 3 Fourier theory II; Fast fourier transform
Thursday, July 5 Fourier transform of Phi(t) and the spectrum thetai of the prime numbers.
Friday, July 6 From the thetai back to pi(x). The Riemann zeta function and the traditional formulation of the Riemann hypothesis.