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• # Artykuł - szczegóły

## Acta Arithmetica

2016 | 173 | 2 | 183-196

## Discrepancy estimates for some linear generalized monomials

EN

### Abstrakty

EN
We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, $([nα]β)_{n≥0}$, is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show in particular that if the pair (α,β) of real numbers is in a certain sense badly approximable, then the discrepancy satisfies a bound of order $𝓞_{α,β,ε}(N^{-1+ε})$.

183-196

wydano
2016

### Twórcy

autor
• Institute of Financial Mathematics, and Applied Number Theory, Johannes Kepler University Linz, Altenbergerstr. 69, A-4040 Linz, Austria
autor
• CNRS Laboratoire Paul Painlevé, Université Lille I, U.M.R. 8524, 59 655 Villeneuve d'Ascq Cedex, France