Related papers: The Brumer--Stark Conjecture over Z

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.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

We prove the Aharoni Berger Conjecture

In this paper the circulant Hadamard conjecture is proved.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We state the Brumer-Stark conjecture and motivate it from two perspectives. Stark's perspective arose in his attempts to generalize the classical Dirichlet class number formula for the leading term of the Dedekind zeta function at $s=1$…

In this paper, we prove a conjecture of Schnell in the surface case.

The article presents the proof of Casas-Alvero conjecture.

The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

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…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

We give a systematic method of providing numerical evidence for higher order Stark-type conjectures such as (in chronological order) Stark's conjecture over $\mathbb{Q}$, Rubin's conjecture, Popescu's conjecture, and a conjecture due to…

We prove an infinitary version of the Brauer-Schur theorem.