On the Root of Unity Ambiguity in a Formula for the Brumer--Stark Units
Matthew H. L. Honnor
TL;DR
This paper proves a conjectural formula for Brumer--Stark units, resolving root of unity ambiguities and removing previous assumptions, thus advancing the understanding of these algebraic units.
Contribution
It provides a complete proof of the Brumer--Stark units formula, eliminating the root of unity ambiguity and simplifying prior assumptions.
Findings
Resolved the root of unity ambiguity in the formula
Confirmed the formula's correctness without additional assumptions
Strengthened the theoretical foundation of Brumer--Stark units
Abstract
We prove a conjectural formula for the Brumer--Stark units. Dasgupta--Kakde have shown the formula is correct up to a bounded root of unity. In this paper we resolve the ambiguity in their result. We also remove an assumption from Dasgupta--Kakde's result on the formula.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · advanced mathematical theories