Distribution mod 1 of additive functions on the set of divisors
Distribution of arithmetical functions. A survey
Distribution of closed geodesics on the modular surface and quadratic irrationals
Distribution of coefficients of Eisenstein series in residue classes
Distribution of consecutive modular roots of an integer
Distribution of difference between inverses of consecutive integers modulo .
Distribution of digits in integers: fractal dimensions and zeta functions
Distribution of integer partitions with large number of summands
Distribution of integers that are sums of three squares of primes
Distribution of irregular pairs
Distribution of irregular prime numbers.
Distribution of lattice points on hyperbolic surfaces
Let two lattices have the same number of points on each hyperbolic surface . We investigate the case when Λ’, Λ” are sublattices of of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.
Distribution of Lévy constants for quadratic numbers
Distribution of Mordell-Weil ranks of families of elliptic curves
We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
Distribution of points on arcs.
Distribution of primes and a weighted energy problem.
Distribution of quadratic non-residues which are not primitive roots
In this article we study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo or for an odd prime and an integer.
Distribution of residues modulo p
Distribution of roots of polynomial congruences.
Distribution of solutions of diophantine equations , where are polynomials