Related papers: The Marker-Steinhorn Theorem
In this short paper we review and extract some features of the Fredholm Alternative problem .
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…
We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
We obtain some results related to Romanoff's theorem.
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
We prove a second main theorem for elliptic projective planes.
The following is proven using arguments that do not revolve around the Riemann Hypothesis or Sieve Theory. If $p_n$ is the $n^{\rm th}$ prime and $g_n=p_{n+1}-p_n$, then $g_n=O({p_n}^{2/3})$.
We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from…
We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.
The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. In this paper, we pose a new problem related to these…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We provide new sufficient conditions under which Ryser's conjecture holds.
This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.