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SUMMARY:Quantum chaology and the music of the primes - Michael Berry (Univ
 ersity of Bristol)
DTSTART:20220912T090000Z
DTEND:20220912T100000Z
UID:TALK178085@talks.cam.ac.uk
DESCRIPTION:The Riemann hypothesis can be interpreted as stating that the 
 prime numbers contain 'music'\, whose component frequencies are the Rieman
 n zeros. The question "Frequencies of what?" leads to tantalizing connecti
 ons with the energy levels of quantum systems whose corresponding classica
 l motion is chaotic. At the level of statistics\, predictions for the Riem
 ann zeros based on semiclassical quantum asymptotics (with primes as perio
 ds of classical trajectories) have reached a high degree of accuracy and r
 efinement. For the zeros themselves\, the Riemann-Siegel formula and its i
 mprovements lead to alternative ways of calculating quantum levels.
LOCATION:No Room Required
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