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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

3 votes

Number-theoretic congruences with geometry and topology?

I'm not sure if this falls under "geometric method", but Mike Hopkins obtained a mod 24 congruence among modular forms by using the theory of topological modular forms (see his 2002 ICM talk, Theorem …
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