Related papers: The Marker-Steinhorn Theorem
The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
The Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
We show the pointwise version of the Ste\v{c}kin theorem on approximation by de la Vall\'ee-Poussin means. The result on norm approximation is also derived.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
In this note we prove an inequality involving primes and the product of consecutive primes.
In this work, we state and prove versions of the linear and bilinear $T(b)$ theorems involving quantitative estimates, analogous to the quantitative linear $T(1)$ theorem due to Stein.
We prove a result on the existence of linear forms of a given Diophantine type.
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
We give a counter example to the new theorem that appeared in the survey \cite{H} on Artin approximation. We then provide a correct statement and a proof of it.
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
We prove a stability version of the Pr\'ekopa-Leindler inequality.