On the Distribution of Square-Full and Cube-Full Integers.
On the Distribution of Square-full and Cube-full Numbers.
On the distribution of subsets of primes in the prime factorization of integers
On the distribution of the divisor function in arithmetic progressions
On the distribution of the Euler function of shifted smooth numbers
We give asymptotic formulas for some average values of the Euler function on shifted smooth numbers. The result is based on various estimates on the distribution of smooth numbers in arithmetic progressions which are due to A. Granville and É. Fouvry & G. Tenenbaum.
On the distribution of the partial sum of Euler's totient function in residue classes
We investigate the distribution of (which counts the number of Farey fractions of order n) in residue classes. While numerical computations suggest that Φ(n) is equidistributed modulo q if q is odd, and is equidistributed modulo the odd residue classes modulo q when q is even, we prove that the set of integers n such that Φ(n) lies in these residue classes has a positive lower density when q = 3,4. We also provide a simple proof, based on the Selberg-Delange method, of a result of T. Dence and...
On the distribution of the values of an additive arithmetical function with values in a locally compact abelian group
On the distribution of the values of Euler's function
On the distribution of the zeros of Dirichlet's L-functions
On the divisor function over Piatetski-Shapiro sequences
Let be an integer part of and be the number of positive divisor of . Inspired by some results of M. Jutila (1987), we prove that for , where is the Euler constant and is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.
On the divisor problem: Moments of Δ(x) over short intervals
On the divisors of
On the equation x² + dy² = Fₙ
On the error function in the asymptotic formula for the counting function of k-full numbers
On the Error Term for the Counting Functions of Finite Abelian Groups.
On the error term in the linear sieve
On the error term in Weyl's law for Heisenberg manifolds
On the error term of an asymptotic formula of Ramanujan
On the error term of the logarithm of the lcm of a quadratic sequence
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma [5] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [3].
On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas
For a prime p > 2, an integer a with gcd(a,p) = 1 and real 1 ≤ X,Y < p, we consider the set of points on the modular hyperbola . We give asymptotic formulas for the average values and with the Euler function φ(k) on the differences between the components of points of .