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Quantum chaology and the music of the primes

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  • UserMichael Berry (University of Bristol)
  • ClockMonday 12 September 2022, 10:00-11:00
  • HouseNo Room Required.

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AR2W01 - Physical resurgence: On quantum, gauge, and stringy

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 alternative ways of calculating quantum levels.

This talk is part of the Isaac Newton Institute Seminar Series series.

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