GOLDBACH-RIEMANN CONNECTIONS THROUGH THE LANGLANDS PROGRAM: An Interdisciplinary Approach to Additive-Multiplicative Unification

This research proposal presents a groundbreaking approach to one of mathematics' most fundamental questions: connecting additive and multiplicative aspects of number theory through the Langlands program. Building on the author's previous work on Riemann-Goldbach equivalences, this interdisciplinary framework proposes to explore whether the Goldbach function r₂(n) can be expressed in the language of modular forms, L-functions, and Galois representations. Key innovations include:- First systematic exploration of Goldbach-Langlands connections- Development of "additive Galois representations" - Computational methodology combining massive data analysis with deep theory- Modular approach allowing partial success across multiple objectives The proposal outlines a 36-month research program with detailed methodology, risk assessment, and collaboration opportunities. Whether successful or not, this work promises valuable contributions to computational number theory, interdisciplinary methodology, and our understanding of arithmetic structures. Suitable for mathematicians, research institutions, and funding agencies interested in frontier research at the intersection of additive number theory, the Langlands program, and computational mathematics.