Proposal: Implementing Vivar Operator for high-precision L-function derivatives (BSD high-rank validation)

[JEAN CARLOS]

Hi sage-devel community,

I have been developing a computational framework for the numerical analysis of L-functions, specifically targeting the stability of derivatives in high-rank cases (the BSD Conjecture context).

I've implemented what I call the Vivar Operator, which uses Abel-regularization and complex phase rotation to identify a stability plateau in the infinitesimal limit epsilon -> 0. In my tests, I have achieved an invariance delta of < 10^-14 for the Elkies curve (r=28) using 1000 dps.

I believe this approach could be a valuable addition to the sage.schemes.elliptic_curves module, particularly for verifying rank and L-series values where standard methods encounter numerical noise.

I would like to share my current Python/mpmath implementation for review and discuss how this methodology could be integrated or used as a validation suite within Sage:

Repository: https://github.com/jean020889/Vivar-Operator-BSD-Stability

Documentation: https://zenodo.org/records/19447612

I am looking forward to your technical feedback on the convergence stability and potential implementation as a Sage module.

Best regards,

Jean Carlos Vivar Benítez

ORCID: 0009-0004-1739-7945