Article
On the Distribution of Rational Functions on Consecutive Powers
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Abstract
We show that for a prime p and any nontrivial rational function r(X) ∈ IFp(X) over the finite field IFp of p elements, the fractional partsr(x) r(xm) , . . . , , p p where x runs through the fields elements which are not the poles of the above functions, are asymptotically uniformly distributed in the m-dimensional unit cube for any fixed m and p → ∞.
Keywords
Rational functions, exponential sums.
Citation
Gutierrez, J. & Shparlinski, I. E. (2008). On the distribution of rational functions on consecutive powers. Uniform Distribution Theory, 3(1), 85–91.
J. Gutierrez and I. E. Shparlinski, “On the distribution of rational functions on consecutive powers,” Uniform Distribution Theory, vol. 3, no. 1, pp. 85–91, 2008.
Gutierrez J, Shparlinski IE. On the distribution of rational functions on consecutive powers. Uniform Distribution Theory. 2008;3(1):85–91.
Gutierrez, J. and Shparlinski, I. E. (2008), ‘On the distribution of rational functions on consecutive powers’, Uniform Distribution Theory, 3(1), pp. 85–91.
Gutierrez, Jaime, and Igor E. Shparlinski. “On the Distribution of Rational Functions on Consecutive Powers.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 85–91.
Gutierrez, Jaime, and Igor E. Shparlinski. “On the Distribution of Rational Functions on Consecutive Powers.” Uniform Distribution Theory 3, no. 1 (2008): 85–91.
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Published by: Engineering Journals
