Related papers: On the Erdos-Fuchs theorem
We provide infinitely many solutions of a Dirichlet problem on balls.
This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.
We obtain some inequalities which are stronger than the Schur majorization inequalities.
In this note, we prove an $L^2$ Hartogs-type extension theorem for unbounded domains.
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
We proove a Bloch's theorem in an almost complex projective plane.
We sketch several proofs of F\'ary--Milnor theorem.
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
We present a proof of a multidimensional version of Peres-Schlag's theorem on Diophantine approximations with lacunary sequences.
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
We prove some new results related to Tanaka's formula.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
We prove a result on the existence of linear forms of a given Diophantine type.
We present a short and self-contained proof of the choosability version of Brooks' theorem.