What question did this study set out to answer?

The goal is to create a universal framework for encoding various mathematical structures related to L-functions and modular forms.

March 27, 2026Open Access

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

Universal framework for encoding Dirichlet characters, Hecke characters, and automorphic representations into bounded fractal potentials on ℝᵈ. Preserves essential arithmetic structure (periodicity, multiplicativity, conductor information) while remaining amenable to spectral analysis. Applications to Landau-Siegel zeros, BSD conjecture, and automorphic L-functions.

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

Key Points

Abstract

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