Related papers: Yet another proof of Brooks' theorem
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…
The paper presents a counterexample to the Hodge conjecture.
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.
We describe how the use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem using limit linear series. As suggested by the degeneration,…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.
In this note we give generalizations and prove 'minimalistic' refinements of the t-birational Section Conjecture (t-BSC), cf. [Be], by doing both: First, by extending the class of base fields over which the t-BSC holds, and second, by…
It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.
We give a proof of some small weight and level cases of Serre's conjecture.
This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note…
A proof is given of Rosenthal's \(\ell_1\) theorem.
Baker's method, relying on estimates on linear forms in logarithms of algebraic numbers, allows one to prove in several situations the effective finiteness of integral points on varieties. In this article, we give a generalisation of…
We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…
We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.
In this paper we show that Cardanos formula for the solution of cubic equations can be reduced to expressions involving only square roots if the real root is rational.
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
This is the continuation of the article by the author that proves a broader class of families admitting the theorem of restriction of sections other than Abelian varieties and gives new examples of pseudo-N\'eron models. In this work, we…