2025/11/17 by Smith, Trey
Mathematics · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Advanced Mathematical Identities
paper · doi:10.48550/arxiv.2511.14810
We propose a generalization of the Elliott-Halberstam conjecture concerning the distribution of prime pairs in arithmetic progressions. This conjecture, which we call the Generalized Elliott-Halberstam Conjecture for Shifted Convolutions (GEH-2), provides a level of distribution for correlations of the von Mangoldt function. We show that GEH-2 implies the twin prime conjecture, describe heuristic and analytic motivation, and discuss implications for prime gaps and k-tuple patterns.