Discrepancy estimates for generalized polynomials.

We obtain an upper bound for the discrepancy of the sequence ([p(n)α]β)n≥0<inline-graphic></inline-graphic> generated by the generalized polynomial [p(x)α]β<inline-graphic></inline-graphic>, where p(x) is a monic polynomial with real coefficients, α<inline-graphic></inline-graphic> and β<inline-graphic></inline-graphic> are irrational numbers satisfying certain conditions. [ABSTRACT FROM AUTHOR]