A generalized formula of Hardy.
A Linear Algorithm for Construction of Optimal Digital Convex 2k-gons
A note on Boolean lattices and Farey sequences.
A note on Boolean lattices and Farey sequences. II.
A note on Farey fractions with denominators in arithmetic progressions
A problem of Erdős-Szüsz-Turán on diophantine approximation
A uniform version of Jarník's theorem
An integral recurrence for sums of powers.
Auszug eines Schreibens an Herrn Stern über die "Verallgemeinerung einer Jacobischen Formel".
Calcul de la dynamique de transformations linéaires contractantes mod 1 et arbre de Farey
Exponential Sums with Farey Fractions
For positive integers m and N, we estimate the rational exponential sums with denominator m over the reductions modulo m of elements of the set ℱ(N) = {s/r : r,s ∈ ℤ, gcd(r,s) = 1, N ≥ r > s ≥ 1} of Farey fractions of order N (only fractions s/r with gcd(r,m) = 1 are considered).
Farey fractions and sums over coprime pairs
Farey fractions with prime denominators
Farey series and the Riemann hypothesis
Hyper-sums of powers of integers and the Akiyama-Tanigawa matrix.
Iterative operators for Farey tree
Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves
We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of bounded height....
Lower bounds for sums of powers of different natural numbers expressed as functions of the sum of these numbers.
Moessnerian theorems. How to prove them by simple graph theoretical inspection.
Natural numbers n for which ⌊nα + s⌋ ≠ ⌊nβ + s⌋