Waring's problem for pseudo-polynomials

Manfred G. Madritsch

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arXiv · 2601.10351

Waring's problem for pseudo-polynomials

Manfred G. Madritsch

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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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Manfred G. Madritsch. 2026-01-15. Waring's problem for pseudo-polynomials. https://arxiv.org/abs/2601.10351

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