Related papers: Primes in tuples and Romanoff's theorem

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…

We establish a superpolynomial lower bound on the range of the permanent function on the set of $n\times n$ matrices with $\pm1$ entries.

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

The Hardy--Littlewood prime $k$-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made…

In this paper, we propose a new primality test, and then we employ this test to find a formula for {\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as…

In this article we prove a general theorem which establishes the existence of limiting distributions for a wide class of error terms from prime number theory. As a corollary to our main theorem, we deduce previous results of Wintner (1935),…

We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian submersion. The latter applies also to the case of…

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at…

We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.

We first give an improved lower bound for the deterministic online simulation of tapes or pushdown stores by queues. Then we inspect some proofs in a classical work on queue machines in the area of Formal Languages and outline why a main…

We give two improved explicit versions of the prime number theorem for primes in arithmetic progression: the first isolating the contribution of the Siegel zero and the second completely explicit, where the improvement is for medium-sized…

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces to finite modular group algebras.

We present upper bounds on certain sums which are related to Artin's primitive root conjecture and are also used in counting ray class characters.

We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem. Using…

We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random…

Motivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers $n\le N$ and integer parts of polynomials evaluated at $n$. The error…