INFINITELY MANY ZEROS OF ζ ( s ) LIE ON
نویسنده
چکیده
ζ(0 + it) = O(|t| 1 2 + ), for each > 0. Apply the Phragmén–Lindelöf Theorem to ζ(s) in a small interval containing 1. Clearly, we can make the linear function arising from the Phragmén–Lindelöf Theorem to pass arbitrarily close to 0 at σ = 1. Thus, as |t| → ∞, ζ(1 + it) = O(|t| ), for each > 0. To apply the Phragmén–Lindelöf Theorem to ζ(s) in the strip 0 ≤ σ ≤ 1, we set k(σ) = aσ + b. Thus, k(0) = 1 2 + = b, k(1) = = a+ b = a+ 1 2 + .
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تاریخ انتشار 2013