arXiv subjects

Matthew H. L. Honnor

Publications and source records attributed to Matthew H. L. Honnor.

4 recordsLinked to original sources

arXiv2025

Comparing Two Formulas for the Gross-Stark Units

Let $F$ be a totally real number field. Dasgupta conjectured an explicit $p$-adic analytic formula for the Gross-Stark units of $F$. In a later paper, Dasgupta-Spiess conjectured a cohomological formula for the principal minors and the characteristic polynomial of the Gross regulator matrix associated to a totally odd character of $F$. Dasgupta-Spiess conjectured that these conjectural formulas coincide for the diagonal entries of Gross regulator matrix. In this paper, we prove this conjecture when $F$ is a cubic field.

math.NT↗

arXiv2025

On the Equality of Three Formulas for Brumer--Stark Units

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 the other two formulas.

math.NT↗

arXiv2025

On the Root of Unity Ambiguity in a Formula for the Brumer--Stark Units

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.

math.NT↗

arXiv2025

On the refined `Birch--Swinnerton-Dyer type' conjectures of Mazur and Tate

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 the predictions of Mazur and Tate, is via the `rank-zero component' of the relevant case of the equivariant Tamagawa Number conjecture.

math.NT↗