On the Simultaneous Distribution of the Fractional Parts of Different Powers of Prime Numbers, Original Research Article

In this paper we study the distribution modulo 1 of the sequence of vectors (pα1, …, pαk), where kgreater-or-equal, slanted2 is a fixed integer and α1, …, αk are fixed real numbers lying in the interval (0, 1) and p runs over the set of prime numbers.