{"id":"palomar/PALOMAR-2026-09-27-000001","url":"https://github.com/jconorgrogan/prime-minor-arcs-2-15/tree/f369f267b4dcfebf010c8e7baa2c9602e2960eba","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-27-000001-v1.json","repo":"https://github.com/jconorgrogan/prime-minor-arcs-2-15","tags":["math.NT","msc:11N37","analytic-number-theory","primes","exponential-sums","circle-method"],"score":0,"title":"Uniform Minor-Arc Cancellation for Primes at the X^{2/15+ε} Scale","trust":"high","domain":"math.NT","source":"palomar","authors":["Conor Grogan"],"reviews":0,"subject":"math.NT","summary":"We prove uniform cancellation in prime-weighted exponential sums at the 2/15 scale, improving the 8/33 local Fourier scale in the Matomäki–Radziwiłł–Tao machinery for averaged prime-pair correlations. On the minor-arc part of every centered arc of radius 1/(2H), the squared von Mangoldt exponential sum over X 0 and epsilon > 0, once H >= X^(2/15+epsilon) and X is large enough. The center may lie anywhere on the circle. The same cutoffs and constants work for every center and are chosen before X and H. This gives uniform minor-arc cancellation at the 2/15 threshold. Since 2/15 < 8/33, the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"formalizes":[{"title":"Prime Pairs at the Prime Number Theorem Threshold: Hardy--Littlewood for Almost Every Shift in Every Interval of Length X^(2/15+epsilon)","identifier":"","relationship":"formalizes"}]}