Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424356 | European Journal of Combinatorics | 2013 | 18 Pages |
Abstract
In this paper we provide in Fp expanding lower bounds for two variables functions f(x,y) in connection with the product set or the sumset. The sum-product problem has been immensely studied in the recent past. A typical result in Fpâ is the existence of Î(α)>0 such that if |A|âpα then max(|A+A|,|Aâ A|)â«|A|1+Î(α), Our aim is to obtain analogous results for related pairs of two-variable functions f(x,y) and g(x,y): if |A|â|B|âpα then max(|f(A,B)|,|g(A,B)|)â«|A|1+Î(α) for some Î(α)>0.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Norbert Hegyvári, François Hennecart,