Let f is an element of Q(x) be a non-constant rational function. We consider 'Waring's problem for f(x),' i.e., whether every element of Q can be written as a bounded sum of elements of {f(a) vertical bar a is an element of Q}. For rational functions of degree 2, we give necessary and sufficient conditions. For higher degrees, we prove that every polynomial of odd degree and every odd Laurent polynomial satisfies Waring's problem. We also consider the 'easier Waring's problem': whether every element of Q can be represented as a bounded sum of elements of {+/- f(a) vertical bar a is an element of Q}.

- Publisher
- OXFORD UNIV PRESS

- Issue Date
- 2020-06

- Language
- English

- Article Type
- Article

- Citation
QUARTERLY JOURNAL OF MATHEMATICS, v.71, no.2, pp.439 - 449

- ISSN
- 0033-5606

- Appears in Collection
- MA-Journal Papers(저널논문)

- Files in This Item
- There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.