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The quantitative behaviour of polynomial orbits on nilmanifol...

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  • ergodicpnt

    ErgodicPNT

    7 members,176 bookmarks

    Ergodic Prime Number Theory This online bookmark is provided for the study of primes and the related topics, such as Riemann Hypothesis and Automorphic L-function, which is the analytic models for primes.

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Saved by 1 people (0 private), first by anonymouse user on 2008-07-15


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For instance, the question of whether (10^n \pi)_{n \in {\Bbb N}} is equidistributed mod 1 is an old unsolved problem, equivalent to asking whether \pi is normal base 10.

Highlighted by arithwsun

For instance, the question of whether (10^n \pi)_{n \in {\Bbb N}} is equidistributed mod 1 is an old unsolved problem, equivalent to asking whether \pi is normal base 10.

Highlighted by arithwsun

[Incidentally, regarding the interactions between physics and number theory: physical intuition has proven to be quite useful in making accurate predictions about many mathematical objects, such as the distribution of zeroes of the Riemann zeta function, but has been significantly less useful in generating rigorous proofs of these predictions. In number theory, our ability to make accurate predictions on anything relating to the primes (or related objects) is now remarkably good, but our ability to actually prove these predictions rigorously lags behind quite significantly. So I doubt that the key to further rigorous progress on these problems lies with physics.]

Highlighted by arithwsun

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