CONDITIONAL on Perelli-Pintz-Salerno 1984 and Perelli-Pintz 1993: Halupczok's ternary Goldbach mean value theorem with primes in progressions and short intervals, repaired
CONDITIONAL on two cited results, both taken as explicit hypotheses of the theorems and never as axioms: PPS1984Remark, the printed Remark on p. 530 of A. Perelli, J. Pintz and S. Salerno, Bombieri's theorem in short intervals, 1984, and PP1993Goldbach, the Goldbach analogue of Theorem 3 of A. Perelli and J. Pintz, On the exceptional set for Goldbach's problem in short intervals, 1993, established in its sections 3 to 5 but not printed as a numbered theorem. These are the inputs that the paper's own proof quotes as its Theorems 2.1 and 2.3. PP1993Goldbach is therefore a weaker citation than…
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