Two estimates on the distribution of zeros of the first derivative of dirichlet L-functions under the generalized 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 B. C. Berndt, N. Levinson, H. L. Montgomery, H. Akatsuka, and the author. Berndt, Levinson, and Montgomery investigated the unconditional case, while Akatsuka and the author gave sharper estimates under the truth of the Riemann hypothesis. Recently, F. Ge improved the estimate on the number of zeros shown by Akatsuka. In this paper, we prove similar results related to the first derivative of Dirichlet L-functions associated with primitive Dirichlet characters under the assumption of the generalized Riemann hypothesis.

Original languageEnglish
Pages (from-to)471-502
Number of pages32
JournalJournal de Theorie des Nombres de Bordeaux
Volume29
Issue number2
DOIs
Publication statusPublished - Jan 1 2017
Externally publishedYes

Fingerprint

Dirichlet L-function
Distribution of Zeros
Riemann hypothesis
Derivative
Zero
Estimate
Dirichlet Character
Riemann zeta function

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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title = "Two estimates on the distribution of zeros of the first derivative of dirichlet L-functions under the generalized riemann hypothesis",
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 B. C. Berndt, N. Levinson, H. L. Montgomery, H. Akatsuka, and the author. Berndt, Levinson, and Montgomery investigated the unconditional case, while Akatsuka and the author gave sharper estimates under the truth of the Riemann hypothesis. Recently, F. Ge improved the estimate on the number of zeros shown by Akatsuka. In this paper, we prove similar results related to the first derivative of Dirichlet L-functions associated with primitive Dirichlet characters under the assumption of the generalized Riemann hypothesis.",
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AB - 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 B. C. Berndt, N. Levinson, H. L. Montgomery, H. Akatsuka, and the author. Berndt, Levinson, and Montgomery investigated the unconditional case, while Akatsuka and the author gave sharper estimates under the truth of the Riemann hypothesis. Recently, F. Ge improved the estimate on the number of zeros shown by Akatsuka. In this paper, we prove similar results related to the first derivative of Dirichlet L-functions associated with primitive Dirichlet characters under the assumption of the generalized Riemann hypothesis.

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