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Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds.

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Zeta function for curves in a manifold

In a slightly different spirit, but still carrying the analogy between closed curves and primes, The Selberg trace formula relates a sum over the lengths of closed geodesics on a hyperbolic surfac …
Richard Montgomery's user avatar