What question did this study set out to answer?

The aim is to explore the spectral properties associated with elliptic curves and their L-functions.

May 6, 2026Open Access

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

View Full Paper

Ask AI

Bookmark

The aim is to explore the spectral properties associated with elliptic curves and their L-functions.
Develop a spectral program around a one-parameter family of Schrödinger operators.
Introduce a bipartite monad constructed from Wach modules and Frobenius idempotents.
Define signed spectral zeta functions and construct a recombination operator.
The spectral trace identity shows relative error better than 1.3 × 10^{-8} for tested curves.
Numerical verification confirms the Witten index equals the algebraic rank across different reduction types.
The spectral regulator aligns with the Néron–Tate regulator to a relative error better than 2 × 10^{-5}.

No takes yet. Share an insight, caveat, or question.

This work demonstrates the connection between the L-function and elliptic curve rank, highlighting the role of Schrödinger operators.

Andrew Timakov (2026) studied this question.

View Full Paper

Ask AI

Bookmark