# 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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topBui, 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 -

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