On the coprimality of values of Euler's function at consecutive integers.
On the correlation of Piltz functions.
On the counting function for the generalized Niven numbers
Given an integer base and a completely -additive arithmetic function taking integer values, we deduce an asymptotic expression for the counting functionunder a mild restriction on the values of . When , the base sum of digits function, the integers counted by are the so-called base Niven numbers, and our result provides a generalization of the asymptotic known in that case.
On the counting function for the Niven numbers
On the density of some sets of primes, IV
On the distribution in the arithmetic progressions of reducible quadratic polynomials in short intervals, II
This paper gives further results about the distribution in the arithmetic progressions (modulo a product of two primes) of reducible quadratic polynomials in short intervals , where now . Here we use the Dispersion Method instead of the Large Sieve to get results beyond the classical level , reaching (thus improving also the level of the previous paper, i.e. ), but our new results are different in structure. Then, we make a graphical comparison of the two methods.
On the distribution of algebraic numbers with prescribed factorization properties
On the distribution of complex-valued multiplicative functions
Let , be complex-valued multiplicative functions. In the paper the necessary and sufficient conditions are indicated for the convergence in some sense of probability measureas .
On the distribution of integers with a fixed number of prime factors.
On the distribution of integers with a given number of prime factors
On the distribution of -integers in Piatetski-Shapiro sequences
A natural number is said to be a -integer if , where and is not divisible by the th power of any prime. We study the distribution of such -integers in the Piatetski-Shapiro sequence with . As a corollary, we also obtain similar results for semi--free integers.
On the distribution of multiplicative arithmetical functions
On the distribution of natural numbers with divisors from an arithmetic progression
On the distribution of perfect totients.
On the distribution of primitive Pythagorean triangles
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 values of Euler's function
On the divisor problem: Moments of Δ(x) over short intervals
On the equation x² + dy² = Fₙ