Abstract
The well-known explicit estimation of the order of the Riemann zeta function
for\(\tfrac{1}{2} \leqslant \sigma \leqslant 1\) andt≧2 (see [3]) is proved with the constantc 1=21. The improvement of the constantc 1 is a consequence of some technical modifications in application of the Vinogradov's inequality for exponential sums with the constant improved byPantelejeva in [1].
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References
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Vinogradov, I. M.: The Method of Trigonometrical Sums in the Theory of Numbers. Moscow: Nauka. 1971 (in Russian).
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Bartz, K.M. On an effective order estimate of the Riemann zeta function in the critical strip. Monatshefte für Mathematik 109, 267–270 (1990). https://doi.org/10.1007/BF01320691
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DOI: https://doi.org/10.1007/BF01320691