Related papers: On the Twin Prime Conjecture
In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.
We survey recent progress in the theory of weak containment of measure preserving group actions.
In this Note, we try to study the relations between the Goldbach Conjecture and the least prime number in an arithmetic progression. We give a new weakened form of the Goldbach Conjecture. We prove that this weakened form and a weakened…
I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.
A brief overview is given of recent progress in understanding the dynamics of hot gauge theories.
In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's…
We discuss some aspects of the theory of subelliptic estimates.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
The problem of the least prime number in an arithmetic progression is one of the most important topics in Number Theory. In [11], we are the first to study the relations between this problem and Goldbach's conjecture. In this paper, we…
We give some results on a priori estimates and on estimates of type sup+inf and sup*inf.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
For integers x and k, let T(x;2k) denote the number of twin prime pairs (p,p+2k) with a distance 2k<=2x**0.5 and p<=x (not p+2k<=x). Let Tg(x;2x**0.5) denote the average of T(x;2k) for all 2k<=2x**0.5. Logically, T(x;2k) should be a…
Associate a unique numerical sequence called the modular signature with each positive integer, using modular residues of each integer under the prime numbers, and distinguishing between the core seed primes and non-core seed primes used to…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…
In this short note we present a family of counterexamples to the King's conjecture.
We adopt a physically motivated empirical approach to the characterisation of the distributions of twin and triplet primes within the set of primes, rather than in the set of all natural numbers. Remarkably, the occurrences of twins or…