On the discrepancy of convex plane sets

József Beck

doi:10.1007/BF01501162

On the discrepancy of convex plane sets

József Beck

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18 Scopus citations

Abstract

Let D₂(N) be the discrepancy function of the class of convex sets in the unit square [0, 1)² as defined in the introduction. A well known result of W. M. Schmidt states that D₂f(N)>const N^1/3. In this paper it is shown that Schmidt's bound is nearly best possible, more precisely, {Mathematical expression}

Original language	English (US)
Pages (from-to)	91-106
Number of pages	16
Journal	Monatshefte für Mathematik
Volume	105
Issue number	2
DOIs	https://doi.org/10.1007/BF01501162
State	Published - Jun 1988
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/BF01501162

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title = "On the discrepancy of convex plane sets",

abstract = "Let D2(N) be the discrepancy function of the class of convex sets in the unit square [0, 1)2 as defined in the introduction. A well known result of W. M. Schmidt states that D2f(N)>const N1/3. In this paper it is shown that Schmidt's bound is nearly best possible, more precisely, {Mathematical expression}",

author = "J{\'o}zsef Beck",

year = "1988",

month = jun,

doi = "10.1007/BF01501162",

language = "English (US)",

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journal = "Monatshefte f{\"u}r Mathematik",

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N2 - Let D2(N) be the discrepancy function of the class of convex sets in the unit square [0, 1)2 as defined in the introduction. A well known result of W. M. Schmidt states that D2f(N)>const N1/3. In this paper it is shown that Schmidt's bound is nearly best possible, more precisely, {Mathematical expression}

AB - Let D2(N) be the discrepancy function of the class of convex sets in the unit square [0, 1)2 as defined in the introduction. A well known result of W. M. Schmidt states that D2f(N)>const N1/3. In this paper it is shown that Schmidt's bound is nearly best possible, more precisely, {Mathematical expression}

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U2 - 10.1007/BF01501162

DO - 10.1007/BF01501162

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EP - 106

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

IS - 2

ER -

On the discrepancy of convex plane sets

Abstract

All Science Journal Classification (ASJC) codes

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