Delphi.science

Helfgott's Proposition 6.2 on the ternary Goldbach minor arcs

Source: github.com/sthubbar/goldbach-lean/tree/d0d978d2cf565be71d69…

Steve Hubbard

Palomar Registrypalomar/PALOMAR-2026-11-03-000029Nov 3, 2026math.NTscore 0

A Lean 4 proof of Lemma 6.1 and Proposition 6.2 of H. A. Helfgott, The ternary Goldbach conjecture is true, arXiv 1312.7748v2, Section 6.1, pages 46 to 48. Lemma 6.1 is a summation by parts bound. Proposition 6.2 turns l2 bounds on S1 over the major arcs and l-infinity bounds on S2 off them into a bound for the integral of |S1|^2 |S2| over the minor arcs, without the factor log x that a plain product of norms would lose. Lemma 6.1 is stated as in the paper. Proposition 6.2 is given in three forms: an abstract measure form with a natural upper endpoint; the arcs of display 3.5 for a finite…

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