4 papers
On the Root of Unity Ambiguity in a Formula for the Brumer--Stark Units
Matthew H. L. Honnor
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…
On the Equality of Three Formulas for Brumer--Stark Units
Samit Dasgupta, Matthew H. L. Honnor, Michael SpieÃ
We prove the equality of three conjectural formulas for the Brumer--Stark units. The first formula has essentially been proven, so the present paper also verifies the validity of t…
Comparing Two Formulas for the Gross-Stark Units
Matthew H. L. Honnor
Let be a totally real number field. Dasgupta conjectured an explicit -adic analytic formula for the Gross-Stark units of . In a later paper, Dasgupta-Spiess conjectured a…
On the refined `Birch--Swinnerton-Dyer type' conjectures of Mazur and Tate
Dominik Bullach, Matthew H. L. Honnor
We prove a substantial part of conjectures of Mazur and Tate that refine the conjecture of Birch and Swinnerton-Dyer. Our approach, which also leads to some results even finer than…