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This research aims to uncover the connections between L-functions and elliptic curves through spectral analysis.

May 6, 2026Open Access

Arithmetic spectroscopy of elliptic curves. Part VI: The supersingular extension and the full spectral BSD formula

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This research aims to uncover the connections between L-functions and elliptic curves through spectral analysis.
Developed a spectral program utilizing Schrödinger operators
Introduced a bipartite monad and defined signed spectral zeta functions
Constructed a recombination operator to manage singularities
Confirmed the residual structure of the spectral zeta function coincides with L(E,s) at s=1
Achieved accurate spectral trace identity with an error of less than 1.3 × 10^{-8}
Numerical tests revealed the Witten index matches the algebraic rank across tested curves

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Implication

This work demonstrates the relationship of the L-function to elliptic curves using Schrödinger operators, indicating a new level of understanding in arithmetic geometry.

Cite This Study

Andrew Timakov (2026) studied this question.

synapsesocial.com/papers/69fa986a04f884e66b53229e https://doi.org/10.5281/zenodo.20030582

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Implication

This work demonstrates the relationship of the L-function to elliptic curves using Schrödinger operators, indicating a new level of understanding in arithmetic geometry.

Arithmetic spectroscopy of elliptic curves. Part VI: The supersingular extension and the full spectral BSD formula

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Discussion

Implication

Cite This Study

Arithmetic spectroscopy of elliptic curves. Part VI: The supersingular extension and the full spectral BSD formula

Key Points

Discussion

Implication

Cite This Study

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