Character-Encoding Potentials Universal Construction for L-Functions and Modular Forms

Key Points

• The goal is to create a universal framework for encoding various mathematical structures related to L-functions and modular forms.
• Developed a framework that utilizes bounded fractal potentials on ℝᵈ.
• Encoded Dirichlet and Hecke characters, along with automorphic representations.
• Maintained key properties such as periodicity and multiplicativity in encoding.
• Preserved essential arithmetic structure in the encoding process.
• Applied the framework to analyze Landau-Siegel zeros and the BSD conjecture, strengthening theories related to L-functions.

Abstract