Related papers: Hasse theorem -- an elementary approach
In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
We prove a variation of Gronwall's lemma.
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
We propose a conjecture, similar to Skolem's conjecture, on a Hasse-type principle for exponential diophantine equations. We prove that in a sense the principle is valid for "almost all" equations. Based upon this we propose a general…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
An elementary introduction to the principles of algebraic surgery.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.
We prove Landen's transformation by a direct elementary transformation of infinite series
In this article, we studied the inverse Erd\H{o}s-Heilbronn problem with the restricted sumset from two components $A$ and $B$ that are not necessarily the same. We give a completely elementary proof for the problem in $\mathbb{Z}$ and some…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
This short note establishes an abstract Hales--Jewett theorem for semigroups equipped with a finite family of retractions. The proof relies on the interplay between retractions and tensor products of ultrafilters.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
In this short paper we review and extract some features of the Fredholm Alternative problem .
We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.
We prove a uniformization theorem in complex algebraic geometry.
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.
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…