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
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
| Original language | English |
|---|---|
| Pages (from-to) | 99-107 |
| Journal | Uniform Distribution Theory |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2017 |