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

33 votes

Computing $\prod_p(\frac{p^2-1}{p^2+1})$ without the zeta function?

An elementary proof of the identity $$ 2 \zeta(2)^2 = 5\zeta(4)$$ has been found by Don Zagier in the paper http://people.mpim-bonn.mpg.de/zagier/files/tex/ConsequencesCohomologySL/fulltext.pdf The …
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