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Discrepancy estimates for some linear generalized monomials

Roswitha Hofer, Olivier Ramaré (2016)

Acta Arithmetica

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, ( [ n α ] 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...

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