On the zeros of the κ-TH derivative of the riemann zeta function under the riemann hypothesis

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Abstract

The number of zeros and the distribution of the real part of non-real zeros of the derivatives of the Riemann zeta function have been investigated by Berndt, Levinson, Montgomery, and Akatsuka. Berndt, Levinson, and Montgomery studied the general case, meanwhile Akatsuka gave sharper estimates for the first derivative of the Riemann zeta function under the truth of the Riemann hypothesis. In this paper, we generalize the results of Akatsuka to the k-th derivative (for positive integer κ) of the Riemann zeta function.

Original languageEnglish
Pages (from-to)69-95
Number of pages27
JournalFunctiones et Approximatio, Commentarii Mathematici
Volume53
Issue number1
DOIs
Publication statusPublished - Dec 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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