Related papers: Casas-Alvero Conjecture is true

We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.

The Casas-Alvero conjecture states that if $f(X)$ is a monic univariate polynomial of degree $d$ over a characteristic $0$ field $\mathbb{K}$ such that $\gcd(f, f_{i})$ is non-trivial for each $i=1, \dots, d-1$, then $f(X)=(X-\alpha)^d$ for…

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

We present a question which implies a complete positive answer for the Bass-Quillen Conjecture.

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

This is a survey on Kawaguchi-Silverman conjecture.

New cases of the multiplicity conjecture are considered.

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 prove a class of normal dilation matrices affirming the Marcus-de Oliveira conjecture.

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

We give a proof of some small weight and level cases of Serre's conjecture.

We answer Kurepa's conjecture on the left factorials in affirmative.

We survey recent developments on the Restriction conjecture.

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.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

Let $z_1,\dots,z_n$ be complex numbers with $|z_j|\le \rho$, where $\rho>1$. Cassels proved that, under an additional restriction on $\rho$, the inequality \[ \prod_{j\ne k}\bigl|1-\overline{z_j}z_k\bigr| \le…

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

We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).