On šnirel'man's constant
On Šnirelman's constant under the Riemann hypothesis
On some universal sums of generalized polygonal numbers
For m = 3,4,... those pₘ(x) = (m-2)x(x-1)/2 + x with x ∈ ℤ are called generalized m-gonal numbers. Sun (2015) studied for what values of positive integers a,b,c the sum ap₅ + bp₅ + cp₅ is universal over ℤ (i.e., any n ∈ ℕ = 0,1,2,... has the form ap₅(x) + bp₅(y) + cp₅(z) with x,y,z ∈ ℤ). We prove that p₅ + bp₅ + 3p₅ (b = 1,2,3,4,9) and p₅ + 2p₅ + 6p₅ are universal over ℤ, as conjectured by Sun. Sun also conjectured that any n ∈ ℕ can be written as and 3p₃(x) + p₅(y) + p₇(z) with x,y,z ∈ ℕ; in...
On sums of five almost equal prime squares
On sums of powers and a related problem
On sums of primes from Beatty sequences.
On sums of seven cubes of almost primes
On the additive complements of the primes and sets of similar growth
On the additive completion of primes
On the almost Goldbach problem of Linnik
Under the Generalized Riemann Hypothesis, it is proved that for any there is depending on only such that every even integer is a sum of two odd primes and powers of .
On the estimation of Schnirelman's constant.
On the exceptional set for the -twin primes problem
On the exceptional set of Goldbach numbers in a short interval
On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables
We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer.
On the Goldbach conjecture and the consistency of general recursive arithemetic.
On the integers not of the form
On the irregularity of the distribution of the sums of pairs of odd primes.
On the number of representations in the Waring-Goldbach problem with a prime variable in an arithmetic progression
We prove a Bombieri-Vinogradov type theorem for the number of representations of an integer in the form with prime numbers such that , under suitable hypothesis on for every integer .
On the number of solutions of N - p = Pr.