On the distribution of the distances of multiples of an irrational number to the nearest integer
On the distribution of the elliptic subset sum generator of pseudorandom numbers.
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
On the distribution of the -Euler polynomials and the -Genocchi polynomials of higher order.
On the distribution of the roots of polynomial
We consider the polynomial for which arises as the characteristic polynomial of the -generalized Fibonacci sequence. In this short paper, we give estimates for the absolute values of the roots of which lie inside the unit disk.
On the divisibility properties of integers (I)
On the divisibility properties of sequences of integers (II)
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 divisors of
On the entry sum of cyclotomic arrays.
On the equation
On the equation aX⁴-bY² = 2
On the equation
On the equation x² + dy² = Fₙ
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 of Fibonacci numbers.
On the existence of a density
On the expansion of Fibonacci and Lucas polynomials.
On the Exponent Average of Integer Sequences.
On the Farey fractions with denominators in arithmetic progression.