Add to ORKGThe paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in this subset is constant and not equal to zero.Comment: 20 page
The counting functions of prime pairs are derived. The asymptotic behavior of the prime pair countin...
International audienceLet π(x) be the number of primes not exceeding x. We produce new explicit boun...
The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1}...
summary:This paper generalizes some results from another one, namely [3]. We have studied the issues...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
Let $d_S$ denote the arithmetic density of a subset $S \subseteq \mathbb N$. We derive a power serie...
We prove an explicit formula to count the partitions of $n$ whose product of the summands is at most...
Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,....
12 páginas.In this note, we show that the set of n such that the arithmetic mean of the first n prim...
An asymptotic formula is derived for the sum of powers of reciprocals of pi(n), where pi(x) denotes ...
We illustrate how elementary information-theoretic ideas may be employed to provide proofs for well-...
Among the thousands of discoveries made by mathematicians over the centuries, some stand out as sign...
In this paper, we give a new upper bound for the number $N_{\mathcal{R}}$ which is defined to be the...
Inverse problems study the structure of a set A when the A + A is “small”. In the article, the struc...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
The counting functions of prime pairs are derived. The asymptotic behavior of the prime pair countin...
International audienceLet π(x) be the number of primes not exceeding x. We produce new explicit boun...
The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1}...
summary:This paper generalizes some results from another one, namely [3]. We have studied the issues...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
Let $d_S$ denote the arithmetic density of a subset $S \subseteq \mathbb N$. We derive a power serie...
We prove an explicit formula to count the partitions of $n$ whose product of the summands is at most...
Let $A$ be a set of natural numbers and let $S_{n,A}$ be the set of all permutations of $[n]=\{1,2,....
12 páginas.In this note, we show that the set of n such that the arithmetic mean of the first n prim...
An asymptotic formula is derived for the sum of powers of reciprocals of pi(n), where pi(x) denotes ...
We illustrate how elementary information-theoretic ideas may be employed to provide proofs for well-...
Among the thousands of discoveries made by mathematicians over the centuries, some stand out as sign...
In this paper, we give a new upper bound for the number $N_{\mathcal{R}}$ which is defined to be the...
Inverse problems study the structure of a set A when the A + A is “small”. In the article, the struc...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
The counting functions of prime pairs are derived. The asymptotic behavior of the prime pair countin...
International audienceLet π(x) be the number of primes not exceeding x. We produce new explicit boun...
The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1}...