The structure of rational functions of two real variables which take few distinct values on large (finite) Cartesian products is described. As an application, a problem of G. Purdy is solved on finite subsets of the plane which determine few distinct distances.
On Exponential Sums with Sparse Polynomials and Rational Functions
β Scribed by Igor Shparlinski
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 476 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
We obtain estimates of complete rational exponentials sums with sparse polynomials and rational functions f (x)=a 1 x r1 + } } } +a t x rt depending on the number of non zero coefficients t rather than on the degree.
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