The Langlands Program in Mathematics Connecting Number Theory and Harmonic Analysis
The Langlands Program establishes a deep correspondence between modular forms in harmonic analysis and objects such as elliptic curves or Galois representations in number theory via the principle of functoriality. This framework posits that L-functions associated with these disparate mathematical structures are intimately linked, allowing properties from one domain (e.g., symmetries) to predict coefficients in another (e.g., prime distribution). Representing a potential "Grand Unified Theory" for mathematics, it bridges algebraic geometry and arithmetic through the mechanism of modularity lifting.
The Langlands Program in Mathematics Connecting Number Theory and Harmonic Analysis
The Langlands Program establishes a deep correspondence between modular forms in harmonic analysis and objects such as elliptic curves or Galois representations in number theory via the principle of …