Joint ICTP/SISSA Statistical Physics seminar:
Series of lectures on: 'Singularities and asymptotics'
" Quantum mechanics, chaos, and the music of the primes "
(duration 2 hours)
Starts 10 Jun 2008 12:00
Ends 10 Jun 2008 20:00
Central European Time
Leonardo da Vinci Building Lecture Room B
Strada Costiera, 11
I - 34151 Trieste (Italy)
The Riemann hypothesis can be interpreted as stating that the prime numbers contain 'music', whose component frequencies are the Riemann zeros. The question "Frequencies of what?" leads to tantalizing connections with the energy levels of quantum systems whose corresponding classical motion is chaotic. At the level of statistics, predictions for the Riemann zeros based on semiclassical quantum asymptotics (with primes as periods of classical trajectories) have reached a high degree of accuracy and refinement. For the zeros themselves, the Riemann-Siegel formula and its improvements lead to new ways of calculating quantum levels.
ICTP - Strada Costiera, 11
I - 34151 Trieste Italy (+39) 040 2240 111 firstname.lastname@example.org