Related papers: A proof of Sendov's conjecture
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
We prove some symmetric $q$-congruences.
We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.
A quick proof of Bing's theorem indicated by the title is given. The proof also concludes Gumerov's result on covering degrees of solenoids.
In this paper we introduce and develop the concept of expansivity of a tuple whose entries are elements from the polynomial ring $\mathbb{C}[x]$. As an inverse problem, we examine how to recover a tuple from the expanded tuple at any given…
This is a survey on Kawaguchi-Silverman conjecture.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
We give an proof on the Weinstein conjecture on the cotangent bundles of open manifolds. Its proof is based on Gromov's nonlinear Fredholm alternative.
In this paper, we give a simple counter example to the famous Hodge conjecture.
We present a creative reimagining of Zolotarev's classical proof of the Law of Quadratic Reciprocity.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.
We prove Serban's conjecture which simplifies greatly the expression of the advanced single-particle Green function in the Calogero-Sutherland model. The importance of proving this conjecture is that it reorganizes the form factor in terms…
We prove existence of an invariant measure on a hypergroup.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We give a geometric proof of the Routh's theorem for tetrahedra.
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.