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how M. Berry came to be involved with the Riemann Hypothesis This is taken from Marcus du Sautoy's book The Music of the Primes (Fourth Estate, 2003) p.278: "He became fascinated by prime numbers in the 1980's after reading an article in the Berry's interest in the primes coincided with his growing understanding of the differences between the statistics of energy levels in electrons playing quantum billiards and the [spectra of random matrices]. 'I thought it might be interesting to look again at the story of the Riemann zeros and Dyson's ideas in the light of the new connections with quantum chaos.' Would the special statistics that Berry had discovered in the energy levels of quantum billiards be reflected in the statistics of the zeros of the Riemann zeta [function]? 'I thought it would be very nice to see if the zeros actually behaved in this way, and I did some rough calculations.' But he didn’t have enough data. 'Then I heard of Odlyzko, who'd done these epic calculations. I wrote to him and he was wonderfully helpful. He explained to me that he'd been a little worried because his calculations beyond a certain point had started to show some deviations. He thought he must have made a mistake in his computations.' But Odlyzko did not have the insights of a physicist. When Berry compared the zeros to the energy levels of chaotic quantum billiards, he found a perfect match. The discrepancies that Odlyzko had observed turned out to be the first sign of the difference between the statistics of frequencies in a random [matrix] and the energy levels of chaotic quantum billiards. He had not been aware of this new chaotic quantum system, but Berry recognised it straight away:
the spectral interpretation
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