On a sequence of rational functions
β Scribed by Jean-Paul Allouche
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 327 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider an indefinite inner product on the algebra of rational functions over the complex numbers, and we obtain a coproduct, which is dual of the usual multiplication, that gives a structure of infinitesimal coalgebra on the rational functions. We also obtain a representation of the finite dual
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.
It will be shown that for rational functions the logarithmic part of the integral can be computed in a very simple manner by Buchberger's algorithm.