Summary
The pertinence of convexity arguments in the study of discrepancy of sequences is exhibited. The usefulness of this viewpoint can be twofold. Firstly, it allows the interpretation of the problem of estimating the discrepancy as a problem in convex programming in important cases. Secondly, it helps to restrict the family of sets which have to be considered when evaluating the usual (or extreme) discrepancy and the isotrope discrepancy of sequences. In particular, in the latter case it suffices to look at a rather special class of convex polytopes.
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Entrata in Redazione il 27 maggio 1971.
Some results of this paper were presented in an address delivered at the Conference on Analytic Number Theory, Carbondale, Ill., October 22–24, 1970.
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Niederreiter, H. Discrepancy and convex programming. Annali di Matematica 93, 89–97 (1972). https://doi.org/10.1007/BF02412017
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DOI: https://doi.org/10.1007/BF02412017