On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou
On the switching principle in sieve theory.
On the symmetry of divisor sums functions in almost all short intervals.
On the symmetry of square-free supported arithmetical functions in short intervals.
On the symmetry of the divisor function in almost all short intervals
On the tails of the limiting distribution function of the error term in the Dirichlet divisor problem
On the Tauberian constant in the Ikehara theorem
On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus
For and any sufficiently large odd we show that for almost all there exists a representation with primes mod for almost all admissible triplets of reduced residues mod .
On the third iterates of the φ- and σ-functions
On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers
On the unimodal character of the frequency function of the largest prime factor
The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum value in...
On the upper bound for π₂(x)
On the value distribution of a class of arithmetic functions
This article deals with the value distribution of multiplicative prime-independent arithmetic functions with if is -free ( a fixed integer), else, and . An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.
On the values of Euler's φ-function
On the Values of Multiplicative Functions in Short Intervals.
On the variation of certain fractional part sequences
Let . We prove the following asymptotic formula with , uniformly for .
On the zeros of a class of arithmetical entire functions
On totient abundant numbers.
On twin almost primes
On two conjectures of Kátai