### Abstract

It is proven that there is a two-coloring of the first n integers for which all arithmetic progressions have discrepancy less than const.n^{1/4}. This shows that a 1964 result of K. F. Roth is, up to constants, best possible.

Original language | English (US) |
---|---|

Pages (from-to) | 195-204 |

Number of pages | 10 |

Journal | Journal of the American Mathematical Society |

Volume | 9 |

Issue number | 1 |

State | Published - Jan 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the American Mathematical Society*,

*9*(1), 195-204.

**Discrepancy in arithmetic progressions.** / Matoušek, Jiří; Spencer, Joel.

Research output: Contribution to journal › Article

*Journal of the American Mathematical Society*, vol. 9, no. 1, pp. 195-204.

}

TY - JOUR

T1 - Discrepancy in arithmetic progressions

AU - Matoušek, Jiří

AU - Spencer, Joel

PY - 1996/1

Y1 - 1996/1

N2 - It is proven that there is a two-coloring of the first n integers for which all arithmetic progressions have discrepancy less than const.n1/4. This shows that a 1964 result of K. F. Roth is, up to constants, best possible.

AB - It is proven that there is a two-coloring of the first n integers for which all arithmetic progressions have discrepancy less than const.n1/4. This shows that a 1964 result of K. F. Roth is, up to constants, best possible.

UR - http://www.scopus.com/inward/record.url?scp=0346616868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346616868&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346616868

VL - 9

SP - 195

EP - 204

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

SN - 0894-0347

IS - 1

ER -