On recurrence in positive characteristic

S. Kristensen; A. Jaššová; P. Lertchoosakul; R. Nair

doi:10.1016/j.indag.2014.11.003

On recurrence in positive characteristic

S. Kristensen^*, A. Jaššová, P. Lertchoosakul, R. Nair

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

Let P-. 1 denote the set of primes minus 1. A classical theorem of A Sárko says that any set of natural numbers of positive density contains a pair of elements whose difference belongs to P-. 1. An ergodic approach to questions of this type was given by the fourth author, building on work of H. Furstenberg. In this paper we give a proof of the positive characteristic analogue of this result using the same approach.

Original language	English
Journal	Indagationes Mathematicae
Volume	26
Issue	2
Pages (from-to)	346-354
Number of pages	9
ISSN	0019-3577
DOIs	https://doi.org/10.1016/j.indag.2014.11.003
Publication status	Published - 1 Jan 2015

Keywords

Fields of formal power series
Intersectivity
Invariant measures
Poincaré recurrence
Positive characteristic

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10.1016/j.indag.2014.11.003

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title = "On recurrence in positive characteristic",

abstract = "Let P-. 1 denote the set of primes minus 1. A classical theorem of A S{\'a}rko says that any set of natural numbers of positive density contains a pair of elements whose difference belongs to P-. 1. An ergodic approach to questions of this type was given by the fourth author, building on work of H. Furstenberg. In this paper we give a proof of the positive characteristic analogue of this result using the same approach.",

keywords = "Fields of formal power series, Intersectivity, Invariant measures, Poincar{\'e} recurrence, Positive characteristic",

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AU - Kristensen, S.

AU - Jaššová, A.

AU - Lertchoosakul, P.

AU - Nair, R.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Let P-. 1 denote the set of primes minus 1. A classical theorem of A Sárko says that any set of natural numbers of positive density contains a pair of elements whose difference belongs to P-. 1. An ergodic approach to questions of this type was given by the fourth author, building on work of H. Furstenberg. In this paper we give a proof of the positive characteristic analogue of this result using the same approach.

AB - Let P-. 1 denote the set of primes minus 1. A classical theorem of A Sárko says that any set of natural numbers of positive density contains a pair of elements whose difference belongs to P-. 1. An ergodic approach to questions of this type was given by the fourth author, building on work of H. Furstenberg. In this paper we give a proof of the positive characteristic analogue of this result using the same approach.

KW - Fields of formal power series

KW - Intersectivity

KW - Invariant measures

KW - Poincaré recurrence

KW - Positive characteristic

U2 - 10.1016/j.indag.2014.11.003

DO - 10.1016/j.indag.2014.11.003

M3 - Journal article

AN - SCOPUS:84924620567

SN - 0019-3577

VL - 26

SP - 346

EP - 354

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 2

ER -

On recurrence in positive characteristic

Abstract

Keywords

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