Additive Energy and Irregularities of Distribution
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Abstract We consider strictly increasing sequences (an)n≥1 of integers and sequences of fractional parts ({anα})n≥1 where α ∈ R. We show that a small additive energy of (an)n≥1 implies that for almost all α the sequence ({anα})n≥1 has large discrepancy. We prove a general result, provide various examples, and show that the converse assertion is not necessarily true.
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2017 ◽
Vol 96
(2)
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pp. 177-184
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1977 ◽
Vol 35
◽
pp. 590-591
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1983 ◽
Vol 41
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pp. 70-71
1977 ◽
Vol 35
◽
pp. 68-69
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1976 ◽
Vol 34
◽
pp. 218-219
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