Related papers: The Brumer--Stark Conjecture over Z

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

In this paper, we propose a generalization of a congruence due to Carlitz.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

We give a new proof of Lucas' Theorem in elementary number theory.

In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for the case of C^3 has been finished.

In this paper, the abc conjecture is negated under certain conditions

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.

The goal of this paper is to prove the full geometric Bogomolov conjecture. We first reduce it to the case that the extension of the base fields has transcendence degree 1, and then we prove the later case by intersection theory in…

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Satake correspondence and the analysis of torus fixed points in…

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…

We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin's…

We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.

In a previous paper the second author developed a new approach to the abelian p-adic Stark Conjecture at s=1 and stated some related conjectures. This paper develops and applies techniques using p-adic measures and continued fractions to…

Shuffle algebra has been employed to give a proof of the duality theorem for multiple zeta-star values of height one.

We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.