Related papers: Paul Erd\H os and additive bases
We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
We prove entropic and total variation versions of the Erd\H{o}s-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
In this article we present method of solving some additive problems with primes. The method may be employed to the Goldbach-Euler conjecture and the twin primes conjecture. The presented method also makes it possible to obtain some…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
Previously, we have introduced a very small number of examples of what we call Ouroboros functions. Using our already established theory of Ouroboros spaces and their functions, we will provide a set of families of Ouroboros functions that…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
Erd\H{o}s-Stone Theorem is a well-known result in extremal graph theory which determines the asymptotic behaviour of maximum number of edges in an $n$-vertex $H$-free graph. In 2009, Nikiforov gave a spectral version of Erd\H{o}s-Stone…
Border bases can be considered to be the natural extension of Gr\"obner bases that have several advantages. Unfortunately, to date the classical border basis algorithm relies on (degree-compatible) term orderings and implicitly on reduced…
This is a note on the classical Waring's problem for several homogeneous forms. For positive integers (n,d,r,s), fix a general r-dimensional subspace of degree d forms in n+1 variables. We describe the family of s-sided polar polyhedra of…
This work discusses the Alon-Tarsi number of line graphs and total graphs. In addition, we also discuss the Alon-Tarsi number of some Erdos-Faber-Lovasz (EFL) graphs.
Comment on ``Understanding OR, PS and DR'' [arXiv:0804.2958]
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
In this article, intended for the Handbook of Recursion Theory, we survey recursion theory on the ordinal numbers, with sections devoted to $\alpha$-recursion theory, $\beta$-recursion theory and the study of the admissibility spectrum.
This article provides information on the life and work of the number theorist Arnold Scholz. It is an English translation with modifications of an introduction to the correspondence of Hasse, Scholz and Taussky published in 2016.
Combinatorial and topological aspects of monoids with an absorbing element and their associated algebras are considered. Phd thesis.
We establish new Bombieri-Vinogradov type estimates for a wide class of multiplicative arithmetic functions and derive several applications, including: a new proof of a recent estimate by Drappeau and Topacogullari for arithmetical…
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.