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 Sárközy. 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}.