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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'Farrill Jun 30 '11 at 22:39

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

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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
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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
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Well, all mathematicians are smoking one pipe or another. –  David Hansen Jun 30 '11 at 23:14
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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. –  plusepsilon.de Jul 1 '11 at 9:52