Gaps between zeros of the derivative of the Riemann $\xi$-function

Hung Manh Bui^[1]

• [1] Mathematical Institute University of Oxford Oxford, OX1 3LB England

Journal de Théorie des Nombres de Bordeaux (2010)

• Volume: 22, Issue: 2, page 287-305
• ISSN: 1246-7405

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Abstract

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Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of ${\xi }^{\prime }\left(s\right)$. We prove that a positive proportion of gaps are less than $0.796$ times the average spacing and, in the other direction, a positive proportion of gaps are greater than $1.18$ times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than $0.7203$ ($1.5$, respectively).

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Bui, Hung Manh. "Gaps between zeros of the derivative of the Riemann $\xi $-function." Journal de Théorie des Nombres de Bordeaux 22.2 (2010): 287-305. <http://eudml.org/doc/116404>.

@article{Bui2010,
abstract = {Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of $\xi ^\{\prime\}(s)$. We prove that a positive proportion of gaps are less than $0.796$ times the average spacing and, in the other direction, a positive proportion of gaps are greater than $1.18$ times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than $0.7203$ ($1.5$, respectively).},
affiliation = {Mathematical Institute University of Oxford Oxford, OX1 3LB England},
author = {Bui, Hung Manh},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Riemann’s -function; derivative; Riemann hypothesis; zeros; gaps},
language = {eng},
number = {2},
pages = {287-305},
publisher = {Université Bordeaux 1},
title = {Gaps between zeros of the derivative of the Riemann $\xi $-function},
url = {http://eudml.org/doc/116404},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Bui, Hung Manh
TI - Gaps between zeros of the derivative of the Riemann $\xi $-function
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 2
SP - 287
EP - 305
AB - Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of $\xi ^{\prime}(s)$. We prove that a positive proportion of gaps are less than $0.796$ times the average spacing and, in the other direction, a positive proportion of gaps are greater than $1.18$ times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than $0.7203$ ($1.5$, respectively).
LA - eng
KW - Riemann’s -function; derivative; Riemann hypothesis; zeros; gaps
UR - http://eudml.org/doc/116404
ER -

References

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