Waring's problem for pseudo-polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911377597136896 |
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| author | Madritsch, Manfred G. |
| author_facet | Madritsch, Manfred G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10351 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Waring's problem for pseudo-polynomials Madritsch, Manfred G. Number Theory 11P55 (11D85, 11L07, 11B83) 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. |
| title | Waring's problem for pseudo-polynomials |
| topic | Number Theory 11P55 (11D85, 11L07, 11B83) |
| url | https://arxiv.org/abs/2601.10351 |