Problems in elementary number theory and methods from physics

Question

I was wondering if there are intuitive "physical" arguments to solve problems from number theory (elementary number theory in particular, but also advanced topics).

To make an example, a proof of some equivalences about primes that uses concepts like energy, forces, or something of that kind.

Can you suggest some references on this subject (or make some examples yourself)?

I think it is hard to find application of number theory in physics. Of course its even harder to find applications of number theory in physic that can be solved by "physical" reasoning — miracle173, Sep 30 '14 at 00:08
@miracle173 I think the question is to find applications of physics—or rather, physical thinking—in number theory. This doesn't seem out of the question. — Andrew Dudzik, Sep 30 '14 at 00:11
@O.L. Along similar lines, I think that one could find some interesting connections in the field of mirror symmetry, which is intimately connected both to string theory and to $p$-adic analysis (important in number theory). But surely we can give a better answer than "Go write a Ph.D thesis on one of these topics." — Andrew Dudzik, Sep 30 '14 at 00:13
@Slade Maybe one of the simplest concrete examples would be the proof of the Jacobi triple product identity via the boson-fermion correspondence. — Start wearing purple, Sep 30 '14 at 00:19
@O.L. I still hope there's a slightly simpler example, but wow, that's cool. If you gave a brief summary of the approach, this would be an excellent answer. — Andrew Dudzik, Sep 30 '14 at 00:24
Check these books: [1] M. Levi, The Mathematical Mechanic. Using Physical Reasoning to Solve Problems, Princeton University Press, Princeton NJ, 2009; [2] V. A. Uspenski, Some applications of mechanics to mathematics, Pergamon Press, New York, 1961, pp. 39-48. — , Oct 09 '14 at 13:53
In addition, there are two related questions on Physics Stack Exchange: 1 and 2. — , Oct 09 '14 at 13:54

score 0 · Accepted Answer · answered Sep 30 '14 at 10:01

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A "physical" approach to a possible proof of the Riemann Hypothesis: The Spectrum of Riemannium.

The idea: the zeros of $\zeta$ are "like" the energy levels of an atomic nucleus.

answered Sep 30 '14 at 10:01

Martín-Blas Pérez Pinilla

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Thank you for the reference. – Dal Oct 11 '14 at 21:59

Problems in elementary number theory and methods from physics

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