Related papers: The Path to Recent Progress on Small Gaps Between …
This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.
In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.
This paper gives a survey of the progress on the minimal genus problem since Lawson's survey.
We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations.…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
We call an interval $[x,y]$ in a poset {\em small} if $y$ is the join of some elements covering $x$. In this paper, we study the chains of paths from a given arbitrary (binary) path $P$ to the maximum path having only small intervals. More…
The goal of this paper is to review the advances that were made during the last few decades in the study of the entropy, and in particular the entropy method, for Kac's many particle system.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.
In the present work the existence of some patterns of primes is shown which generalize the celebrated result of Green and Tao according to which there are arbitrarily long arithmetic progressions in the sequence of primes
We generalise Zhang's and Pintz recent results on bounded prime gaps to give a lower bound for the the number of prime pairs bounded by 6*10^7 in the short interval $[x,x+x (\log x)^{-A}]$. Our result follows only by analysing Zhang's proof…
This paper surveys the significant progress over the past couple of decades in the theory of stratified spaces through the application of controlled methods as well as through the application of intersection homology.
We showed that the prime gap for a prime number p is less than or equal to the prime count of the prime number.
In this article we present recent advances on interval methods for rigorous computation of Poincar\'e maps. We also discuss the impact of choice of Poincar\'e section and coordinate system on obtained bounds for computing Poincar\'e map…
A survey paper on some recent results on additive problems with prime powers.
I review the recent progress in small $x$ physics, concentrating on the topics relevant to the BFKL evolution.
We examine the prime gaps using a statistical approach. It is first shown that the Andrica's conjecture is true for half or more cases. Using the arguments of averages, it is further shown that Andrica's conjecture is true. We further…
We prove that there are infinitely often pairs of primes much closer than the average spacing between primes - almost within the square root of the average spacing. We actually prove a more general result concerning the set of values taken…
We review some recent development in the theory of spatial extremes related to Pareto Processes and modeling of threshold exceedances. We provide theoretical background, methodology for modeling, simulation and inference as well as an…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…