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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

Basel problem and inversive geometry

It doesn't quite answer your questions, but there is another change of variables that Zagier and Kontsevich use to evaluate $$\int_{0}^{1} \int_{0}^{1} \frac{1}{4\sqrt{xy} \ (1-xy)} \ dx \ dy.$$ (Se …
Vivek Kaushik's user avatar