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Dear participants (and curios)curious), I'd like to bring your attention to two brand new arXiv papers with new theorems closely related to the original question posed by I. J. Kennedy. The papers are: i1) "An interface between physics and number theory", available at http://arxiv.org/abs/1011.0523v1, and ii2) "New Properties of Fourier Series and Riemann Zeta Function", available at http://arxiv.org/abs/1008.5046v3 . In the first paper, it is shown (with some controversy) that Euler's gamma is a... RATIONAL number!!! The other paper contains an interesting theorem (#22) in which the author shows that the ratio $\zeta(2n+1)/{\pi^{2n+1}}$ does not have an Euler sum. It seems (and I'm now trying to proof) that this means that implies these ratios are then irrational. It would be very interesting to hear the opinion of some great mathematicians specialists (number theorists) -- such as W. Zudilin and Rivoal -- on the validity of these works theorems and my conclusion on the irrationality of the above "zeta ratios"..ratios.

(F. M. S. Lima, University of Brasilia -- fabio{at}fis.unb.br)
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Dear participants (and curios), I'd like to bring your attention to two brand new arXiv papers with new theorems closely related to the original question posed by I. J. Kennedy. The papers are: i) "An interface between physics and number theory", available at http://arxiv.org/abs/1011.0523v1, and ii) "New Properties of Fourier Series and Riemann Zeta Function", available at http://arxiv.org/abs/1008.5046v3 In the first paper, it is shown (with some controversy) that Euler's gamma is a... RATIONAL number!!! The other paper contains an interesting theorem (#22) in which the author shows that the ratio $\Zeta(2n+1)/{\pi^(2n+1)}$ \zeta(2n+1)/{\pi^{2n+1}}$ does not have an Euler sum. It seems that this means that these ratios are then irrational. It would be very interesting to hear the opinion of some great mathematicians such as W. Zudilin on the validity of these works and my conclusion on the irrationality of the above "zeta ratios"... (F. M. S. Lima, University of Brasilia)
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Dear participants (and curios), I'd like to bring your attention to two brand new arXiv papers with new theorems closely related to the original question posed by I. J. Kennedy. The papers are: i) "An interface between physics and number theory", available at http://arxiv.org/abs/1011.0523v1, and ii) "New Properties of Fourier Series and Riemann Zeta Function", available at http://arxiv.org/abs/1008.5046v3 In the first paper, it is shown (with some controversy) that Euler's gamma is a... RATIONAL number!!! The other paper contains an interesting theorem (#22) in which the author shows that the ratio $\Zeta(2n+1)/{\pi^(2n+1)}$ does not have an Euler sum. It seems that this means that these ratios are then irrational. It would be very interesting to hear the opinion of some great mathematicians such as W. Zudilin on the validity of these works and my conclusion on the irrationality of the above "zeta ratios"... (F. M. S. Lima, University of Brasilia)