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arXiv · 2406.09256

Integral solutions to systems of diagonal equations

Nick Rome·Shuntaro Yamagishi
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Abstract

In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We improve the required number of variables compared to previous results by incorporating the recent progress on Waring's problem and the resolution of the main conjecture in Vinogradov's mean value theorem.

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Nick Rome, Shuntaro Yamagishi. 2024-06-13. Integral solutions to systems of diagonal equations. https://doi.org/10.2140/pjm.2026.340.179

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