Related papers: On an average ternary problem with prime powers
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…
A survey paper on some recent results on additive problems with prime powers.
In this paper we extend and improve all the previous results known in literature about weighted average, with Ces\`aro weight, of representations of an integer as sum of a positive arbitrary number of prime powers and a non-negative…
In this note, we approximate the average of prime powers in the decomposition of $n!$ into prime numbers.
We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case $k = 2$ [6] and $k = 3$…
We survey the classical results on the prime number theorem
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (1998).
In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.
In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.
I give some claims on primorial prime numbers for interested readers in number theory.
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be…
We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.
We give a more strong heuristic justification of our conjecture on the excess of the odious primes.
Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers.
We establish Bombieri-Vinogradov's type result for the number of solutions of the ternary Goldbach problem with primes from arithmetic progressions.
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…