article published yes Nick Rome author Shuntaro Yamagishi author 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b TiBr department 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. Mathematical Sciences Publishers2026 eng 0030-8730 1945-5844 2406.0925610.2140/pjm.2026.340.179 3401179-198 N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198. Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1, Mathematical Sciences Publishers, 2026, pp. 179–98, doi:<a href="https://doi.org/10.2140/pjm.2026.340.179">10.2140/pjm.2026.340.179</a>. Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198. Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. 2026;340(1):179-198. doi:<a href="https://doi.org/10.2140/pjm.2026.340.179">10.2140/pjm.2026.340.179</a> N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1. Mathematical Sciences Publishers, pp. 179–198, 2026. Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers, 2026. <a href="https://doi.org/10.2140/pjm.2026.340.179">https://doi.org/10.2140/pjm.2026.340.179</a>. Rome, N., &#38; Yamagishi, S. (2026). Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/pjm.2026.340.179">https://doi.org/10.2140/pjm.2026.340.179</a> 212422026-02-16T15:17:27Z2026-07-16T08:36:20Z