Additive Energy and Irregularities of Distribution
| Autor: | Gerhard Larcher, Christoph Aistleitner |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Condensed Matter::Quantum Gases
Physics Mathematics - Number Theory High Energy Physics::Lattice 010102 general mathematics 0102 computer and information sciences 01 natural sciences Combinatorics Distribution (mathematics) Mathematics - Classical Analysis and ODEs 010201 computation theory & mathematics Classical Analysis and ODEs (math.CA) FOS: Mathematics Mathematics - Combinatorics Number Theory (math.NT) Combinatorics (math.CO) 0101 mathematics Energy (signal processing) |
| Zdroj: | Uniform distribution theory. 12:99-107 |
| ISSN: | 2309-5377 |
| Popis: | We consider strictly increasing sequences $\left(a_{n}\right)_{n \geq 1}$ of integers and sequences of fractional parts $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ where $\alpha \in \mathbb{R}$. We show that a small additive energy of $\left(a_{n}\right)_{n \geq 1}$ implies that for almost all $\alpha$ the sequence $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ has large discrepancy. We prove a general result, provide various examples, and show that the converse assertion is not necessarily true. Comment: 8 pages. To appear in Uniform Distribution Theory |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|