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APPROXIMATION BY SEVERAL RATIONALS

Part of: Multiplicative number theory Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  01 April 2008

IGOR E. SHPARLINSKI
IGOR E. SHPARLINSKI*
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia (email: igor@ics.mq.edu.au)
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Abstract

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Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a1/q1,…,an/qn with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible ranges for the denominators q1,…,qn, one can improve a result of T. H. Chan by using a different approach.

Keywords

rational approximationsmultivariate congruences

MSC classification

Secondary: 11J04: Homogeneous approximation to one number 11N25: Distribution of integers with specified multiplicative constraints
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 325 - 329
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Chan, T. H., ‘Approximating reals by sums of rationals’, Preprint, 2007 (available from http://arxiv.org/abs/0704.2805).Google Scholar
[2]Shparlinski, I. E., ‘On the distribution of points on multidimensional modular hyperbolas’, Proc. Japan Acad. Sci., Ser. A 83 (2007), 5–9.Google Scholar
[3]Shparlinski, I. E., ‘Distribution of inverses and multiples of small integers and the Sato–Tate conjecture on average’, Michigan Math. J. to appear.Google Scholar
[4]Shparlinski, I. E., ‘On a generalisation of a Lehmer problem’, Preprint, 2006 (available from http://arxiv.org/abs/math/0607414).Google Scholar