# Riemann hypothesis and action principle [closed]

Hello,

I would like to know whether the Riemann hypothesis could be a consequence of some kind of action principle: in other words, can the equation $\zeta(s)=0$ be interpreted as the formulation of some number theoretical action principle? Thank you in advance.

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## closed as not a real question by Qfwfq, David Hansen, gowers, Felipe Voloch, José Figueroa-O'FarrillJun 30 '11 at 22:39

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I'll vote "Close as not a real question" until the question isn't further clarified. – Qfwfq Jun 30 '11 at 21:51
So you're asking if there is a functional whose extrema correspond in some reasonable way to the zeros of the zeta function? If so, this is strikes me as a trivial rephrasing of a well-known pipe dream regarding the zeta function: the Hilbert-Polya conjecture. But I am also voting to close. – David Hansen Jun 30 '11 at 22:06
Well, trivial rephrasing or not, if he came up with it idependently, +1, I'd say. After all, some people are still smoking this pipe after all these years. [Hope this continuation on pipe-dream makes sense.] – quid Jun 30 '11 at 23:08
Well, all mathematicians are smoking one pipe or another. – David Hansen Jun 30 '11 at 23:14
Read the Article of Ralf Meyer about adeles and L functions, he gives a spectral interpretation. It's on the arxiv, but here is another link: www.math.uni-muenster.de/sfb/about/publ/heft300.ps . He constructs an operator closely related to the right regular action on the adeles. A right regular action on a locally abelian group is always in close connection with the Fourier transform. – Marc Palm Jul 1 '11 at 9:52