Related papers: Bounded gaps between primes
In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this…
ABSTRACT. In this article we present a point of view that highlights the importance of finding the upper bounds for prime gaps, in order to solve the twin primes conjecture and the Goldbach conjecture. For this purpose, we present a…
This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be described and what can be said about the structure of the universal enveloping A(m)-algebra of an L(m)-algebra,…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…
Classification margins are commonly used to estimate the generalization ability of machine learning models. We present an empirical study of these margins in artificial neural networks. A global estimate of margin size is usually used in…
This is a list of problems that were collected from participants at the Comparative Prime Number Theory Symposium held at UBC from June 17 to June 21, 2024. Its goal is to stimulate research and future collaborations in this growing field.…
The author sharpens a result of Jia (1996), showing that the interval $[n, n+n^{\frac{1}{21.5}+\varepsilon}]$ contains prime numbers for almost all $n$. Watt's mean value bound, a delicate sieve decomposition and more accurate estimates for…
These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as…
These are lecture notes for a course I gave in mid-1990s for MSc students at the University of Bath. It presents an algorithm with singly exponential complexity for the existential theory of the reals, in the spirit of J. Renegar. The aim…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection between Chen's work on iterated integrals on the one hand, and…
This paper has two goals. First, we present the turn-taking annotation layers created for 95 minutes of conversational speech of the Graz Corpus of Read and Spontaneous Speech (GRASS), available to the scientific community. Second, we…
Erd\H{o}s considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotics for all moments. Furthermore, we prove a…
The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
Citation information in scholarly data is an important source of insight into the reception of publications and the scholarly discourse. Outcomes of citation analyses and the applicability of citation based machine learning approaches…
This is a personal tribute to Lance Littlejohn on the occasion of his 70th birthday. It is meant as a present to him for many years of friendship. It is not written in the "Satz-Beweis" style of Edmund Landau or even in the format of a…
We argue that the communication structures in the Chinese social sciences have not yet been sufficiently reformed. Citation patterns among Chinese domestic journals in three subject areas -- political science and marxism, library and…
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.