Algorithmic Proof of the Epsilon Constant Conjecture

TL;DR

This paper presents an algorithmic approach to prove the epsilon constant conjecture for all fields with absolute degree up to 15, providing a computational method for a longstanding mathematical problem.

Contribution

The paper introduces an efficient algorithm for computing local fundamental classes and applies it to prove the epsilon constant conjecture for fields of degree up to 15.

Findings

Successfully proved the epsilon constant conjecture for all fields with degree ≤ 15.

Developed an efficient algorithm for computing local fundamental classes.

Addressed and solved multiple computational problems in the proof process.

Abstract

In this paper we will algorithmically prove the local and global epsilon constant conjectures for all fields of absolute degree lower or equal to 15. To this end we will present an efficient algorithm for the computation of local fundamental classes and address several other problems arising in the algorithmic proof.