Related papers: On Two of Erd\"os's Open Problems
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…
An observation on Hall-Littlewood polynomials.
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.
This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…
This paper concerns the number of lattice points in a circle.
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.
These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.
After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erd\H{o}s-Mirksy conjecture which states that there are infinitely many positive integers…
We study a finite analog of a conjecture of Erd\"os on the sum of the squared multiplicities of the distances determined by an $n$-element point set. Our result is based on an estimate of the number of hinges in spectral graphs.
We give a short proof of a sumset conjecture of Erd\"os, recently proved by Moreira, Richter and Robertson: every subset of the integers of positive density contains the sum of two infinite sets. The proof is written in the framework of…
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
A new tool is introduced, specially tailored for the study of order 2 bases of N. It is called the Erdos-Tuan algebra since it suits well their conjecture.
In this short note, we give an affirmative answer to Wu's conjecture on practical numbers, which was posed in [X.-H. Wu, {\it Special forms and the distribution of practical numbers}, Acta Math. Hungar., {\bf 160}(2020), 405-411].
We have already conjectured 2 important guesses regarding Hypo-Lie algebra and modular simple Lie algebra. We would like to attach 2 important guesses more to this conjecture. Such new guesses are related to the Steinberg module.
Introduction 1. The two-eigenvalue problem 2. Hecke algebra representations of braid groups 3. Duality of Jones-Wenzl representations 4. Closed images of Jones-Wenzl sectors 5. Distribution of evaluations of Jones polynomials 6. Fibonacci…
A simple formal recasting of well known arguments concerning the ordering problems of General Relativity allows to obtain in such a context a Gr\"{o}enewald Van Hove like theorem.