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Arithmetic Progressions in Sets of Fractional Dimension

✍ Scribed by Izabella Łaba; Malabika Pramanik

Publisher
Springer
Year
2009
Tongue
English
Weight
350 KB
Volume
19
Category
Article
ISSN
1016-443X

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Discrepancy of Arithmetic Progressions i
Discrepancy of Arithmetic Progressions in Higher Dimensions
✍ Benedek Valkó 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 136 KB

proved that the discrepancy of arithmetic progressions contained in [1, N]={1, 2, ..., N} is at least cN 1/4 , and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on [1, N] d