Related papers: The prime analog of the Kepler-Bouwkamp constant

We analyse an analog of the entropy-power inequality for the weighted entropy.

For $k\ge1$, a $k$-almost prime is a positive integer with exactly $k$ prime factors, counted with multiplicity. In this article we give elementary proofs of precise asymptotics for the reciprocal sum of $k$-almost primes. Our results match…

We survey the classical results on the prime number theorem

We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.

In this paper we give Kummer's original type congruence relation modulo a prime power for the universal Bernoulli numbers. Although the index of the power is half of original congruence, this estimate is best possible.

We present a new, elementary, dynamical proof of the prime number theorem.

We prove a stability version of the Pr\'ekopa-Leindler inequality.

We discuss an interferometric approach to the estimation of quantum mechanical damping. We study specific classes of entangled and separable probe states consisting of superpositions of coherent states. Based on the assumption of limited…

The Mertens' first theorem gives us the following asymptotic formula \begin{equation*} \sum_{\substack{p\leq x\\ p~prime}}\frac{lnp}{p}=lnx+O(1), \end{equation*} and the Mertens' second theorem indicates that there exists a constant…

We evaluate the Bateman-Horn constant for the polynomial $x^3+x+1$.

In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant…

Let $P$ be the set of all prime numbers, ${q_1},{q_2}, \cdots ,{q_m} \in P$, $P_k$ be the k-th $(k = 1,2, \cdots m)$ element of $P$ in ascending order of size, ${\alpha _1},{\alpha _2}, \cdots ,{\alpha _m}$ be positive integers, and ${\beta…

In this note we prove an inequality involving primes and the product of consecutive primes.

We introduce some generalizations of the Euler-Kronecker constant of a number field and study their arithmetic nature.

For a prime number p greater than 6000, the Olson's constant for the group Z_p+Z_p is given by Ol(Z_p+Z_p)=p-1+Ol(Z_p).

The issue of the cosmological constant is discussed in details and a solution to the problem is suggested.

In classical prime number theory several asymptotic relations are considered to be "equivalent" to the prime number theorem. In the setting of Beurling generalized numbers, this may no longer be the case. Under additional hypotheses on the…

Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…

A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…