Fractional parts of generalized polynomials at prime arguments

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

Let f(X) be a monic polynomial of degree d≥2 with real coefficients. In this paper, we obtain an upper bound for the discrepancy of the sequence ([f(p)α]β) generated by the generalized polynomial [f(X)α]β, where p runs through the set of all primes and α, β are irrational numbers satisfying certain conditions. We also study the small fractional parts of the sequence ([f(p)α]β) and prove a result analogous to that of Madritsch and Tichy (Theorem 2.3, [13]).

DOI

10.1016/j.jmaa.2024.128503

Publication Date

11-1-2024

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