WARING'S PROBLEM FOR RATIONAL FUNCTIONS IN ONE VARIABLE

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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
DOI
10.1093/qmathj/haz052
URI
http://hdl.handle.net/10203/275553
Appears in Collection
MA-Journal Papers(저널논문)
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