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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Discrepancy in arithmetic progressions
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by Jiří Matoušek and Joel Spencer PDF
J. Amer. Math. Soc. 9 (1996), 195-204 Request permission


It is proven that there is a two-coloring of the first $n$ integers for which all arithmetic progressions have discrepancy less than $\mathrm {const}.n^{1/4}$. This shows that a 1964 result of K. F. Roth is, up to constants, best possible.
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Additional Information
  • Jiří Matoušek
  • Affiliation: Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
  • Email:
  • Joel Spencer
  • Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
  • Email:
  • Received by editor(s): February 18, 1994
  • Received by editor(s) in revised form: December 29, 1994
  • Additional Notes: The first author was supported by Charles University grant No. 351 and Czech Republic Grant GAČR 201/93/2167. Part of this research was done during a visit to Princeton University supported by DIMACS
  • © Copyright 1996 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 9 (1996), 195-204
  • MSC (1991): Primary 11B25, 11N37
  • DOI:
  • MathSciNet review: 1311824