On finite pseudorandom binary sequences: functions from a Hardy field

We provide a construction of binary pseudorandom sequencesbased on Hardy fields \(\mathcal{H}\) $\mathcal{H}$ as considered by Boshernitzan. In particular we give upperbounds for the well distribution measure and the correlation measure definedby Mauduit and Sárközy. Finally we show that the correlation measure of order sis small only if s is small compared to the “growth exponent” of \(\mathcal{H}\) $\mathcal{H}$ .