{"id":"hexagon/2610.00380","pdf":"https://hexagonmath.org/pdf/2610.00380v1","url":"https://hexagonmath.org/abs/2610.00380v1","tags":["msc:11N05","msc:11N35","msc:11N36","Harman's sieve","Variable role-reversals","arithmetic progressions","sieve methods"],"score":0,"title":"Note on variable role-reversals","domain":"math.NT","source":"hexagon","authors":["Runbo Li"],"reviews":0,"subject":"math.NT","summary":"In [1], the author uses variable role-reversals only when $\\theta < \\frac{45}{89} - \\varepsilon$. In this note, we shall discuss how to use variable role-reversals when $\\frac{45}{89} - \\varepsilon \\leqslant \\theta < \\frac{11}{20} - \\varepsilon$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}