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Equidistribution of values of rational functions (mod p)

Published online by Cambridge University Press:  14 November 2011

R. W. K. Odoni  and
P. G. Spain
R. W. K. Odoni
Affiliation:
Mathematics Department, University of Glasgow, Glasgow G12 8QW, Scotland, U.K
P. G. Spain
Affiliation:
Mathematics Department, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.; Institute of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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Extract

Let R1(x),…, Rd(x) be rational functions in Iℚ(x), such that 1, R1(x),…, Rd(x) are linearly independent over Iℚ. For almost all primes p, their mod p reductions, are well-defined rational functions over Fp and are linearly independent over Fp We show that asymptotically the points

are uniformly distributed in [0, l)d.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 911 - 929
Copyright
Copyright © Royal Society of Edinburgh 1995

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