dorsal/arxiv
View SchemaWaring's problem for pseudo-polynomials
| Authors | Manfred G. Madritsch |
|---|---|
| Categories | |
| ArXiv ID | 2601.10351vv1 |
| URL | https://arxiv.org/abs/2601.10351 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Waring's problem has a long history in additive number theory. In its original form it deals with the representability of every positive integer as sum of $k$-th powers with integer $k$. Instead of these powers we deal with pseudo-polynomials in this paper. A pseudo-polynomial is a ``polynomial'' with at least one exponent not being an integer. Our work extends earlier results on the related problem of Waring for arbitrary real powers $k>12$ by Deshouillers and Arkhipov and Zhitkov.
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"abstract": "Waring\u0027s problem has a long history in additive number theory. In its original form it deals with the representability of every positive integer as sum of $k$-th powers with integer $k$. Instead of these powers we deal with pseudo-polynomials in this paper. A pseudo-polynomial is a ``polynomial\u0027\u0027 with at least one exponent not being an integer.\n Our work extends earlier results on the related problem of Waring for arbitrary real powers $k\u003e12$ by Deshouillers and Arkhipov and Zhitkov.",
"arxiv_id": "2601.10351",
"authors": [
"Manfred G. Madritsch"
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"math.NT"
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"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Waring\u0027s problem for pseudo-polynomials",
"url": "https://arxiv.org/abs/2601.10351",
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