Abstract
It is shown that the function\(\zeta ^{1/k} \) (s) (k large) can be used to derive the prime number theorem from the known zero-free regions for the Riemann Zeta-function. For the proof no upper bound for |ζ′/ζ(s)| is required.
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Literatur
Ingham, A. E.: The Distribution of Prime Numbers. Cambridge: Univ. Press. 1932.
Prachar, K.: Primzahlverteilung. Berlin-Göttingen-Heidelberg: Springer. 1957.
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Wolke, D. Eine Bemerkung zum Primzahlsatz. Monatshefte für Mathematik 100, 337–339 (1985). https://doi.org/10.1007/BF01339233
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DOI: https://doi.org/10.1007/BF01339233