An Almost-All Theorem for a Restricted Goldbach Sum over Arithmetic Progressions with Explicit Unconditional Constants

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Submitted: May 7, 2026
Published: May 21, 2026
DOI: 10.29328/journal.ijpra.1001152
Keywords:
Goldbach problem, Arithmetic progressions, Restricted Goldbach sums, Almost-all theorem, Explicit constants, Circle method, Vaughan identity, Bombieri-Vinogradov theorem, Dirichlet characters, Singular series, Twin-prime constant, Gallagher-Goldston constant, Minor arcs, Major arcs, Siegel-Walfisz theorem, Exceptional set, Stechkin optimization, Chebyshev inequality, Second moment decomposition, Large sieve inequality, Pintz-type bound, Analytic number theory, Unconditional results, Weighted exponential sums, Euler totient function

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Ibar Federico Anderson
Universidad Nacional de La Plata, La Plata, Argentina

Abstract

In this paper, which is entirely unconditional, we prove a sharpened almost-all theorem with fully explicit effective constants for the restricted weighted Goldbach sum

Article Details

Anderson, I. F. (2026). An Almost-All Theorem for a Restricted Goldbach Sum over Arithmetic Progressions with Explicit Unconditional Constants. International Journal of Physics Research and Applications, 129–140. https://doi.org/10.29328/journal.ijpra.1001152
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Copyright (c) 2026 Anderson IF.

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