Some results in the theory of Riemann sums (Q1364161)

The aim of this paper is to prove negative type results concerning the almost everywhere convergence of Riemann sums along the sequence of primes. An earlier result of \textit{W. Rudin} [Proc. Am. Math. Soc. 15, 321-324 (1964; Zbl 0132.03601)] is improved. \textit{J. Bourgain}'s entropy criterion is used [Isr. J. Math. 63, No. 1, 79-97 (1988; Zbl 0677.60042)]. See also \textit{D. Schneider} and the second author [in: Séminaire de probabilités XXVII. Lect. Notes Math. 1557, 202-206 (1993; Zbl 0799.60035)], concerning the technique of proof.