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Riemann-Siegel theta function says θ(x) = arg ζ(½ + t i), so arg (e− i θ(x) ζ(½ + t i)) = 0. If Im Z(x) = 0 as well, we get θ(x) = 0 or θ(x) = π/2. How is that possible?
Z times Ω does not tend to 0, this is true; but it does not imply that sup {Z(t): t < x} is increasing, and that meaning of the symbol Ω is nonstandard. -- Yecril ( talk) 08:23, 7 October 2008 (UTC)
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Riemann-Siegel theta function says θ(x) = arg ζ(½ + t i), so arg (e− i θ(x) ζ(½ + t i)) = 0. If Im Z(x) = 0 as well, we get θ(x) = 0 or θ(x) = π/2. How is that possible?
Z times Ω does not tend to 0, this is true; but it does not imply that sup {Z(t): t < x} is increasing, and that meaning of the symbol Ω is nonstandard. -- Yecril ( talk) 08:23, 7 October 2008 (UTC)