On finite pseudorandom binary sequences: functions from a Hardy field

We provide a construction of binary pseudorandom sequences based on Hardy fields H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{H}$$\end{document} as considered by Boshernitzan. In particular we give upper bounds for the well distribution measure and the correlation measure defined by Mauduit and S & aacute;rk & ouml;zy. Finally we show that the correlation measure of order s is small only if s is small compared to the "growth exponent" of H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{H}$$\end{document}.