Integral solutions to systems of diagonal equations
Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198.
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Author
Rome, Nick;
Yamagishi, ShuntaroISTA
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Abstract
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 recent progress on Waring’s problem and the resolution of the main conjecture in Vinogradov’s mean value theorem.
Publishing Year
Date Published
2026-01-01
Journal Title
Pacific Journal of Mathematics
Publisher
Mathematical Sciences Publishers
Volume
340
Issue
1
Page
179-198
ISSN
eISSN
IST-REx-ID
Cite this
Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 2026;340(1):179-198. doi:10.2140/pjm.2026.340.179
Rome, N., & Yamagishi, S. (2026). Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2026.340.179
Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2026. https://doi.org/10.2140/pjm.2026.340.179.
N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,” Pacific Journal of Mathematics, vol. 340, no. 1. Mathematical Sciences Publishers, pp. 179–198, 2026.
Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198.
Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” Pacific Journal of Mathematics, vol. 340, no. 1, Mathematical Sciences Publishers, 2026, pp. 179–98, doi:10.2140/pjm.2026.340.179.
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