Farey fractions and sums over coprime pairs

Products of Farey Fractions

Neighboring Fractions in Farey Subsequences

We present explicit formulas for computation of the neighbors of several elements in Farey subsequences.

FGLM and coprime polynomial pairs

To obtain coprime polynomial pairs, it is often used an approach that consists of taking two random polynomials of the required degrees and testing whether they are relatively prime. If they are not, they are discarded and another pair is tried. The test can obviously be carried out very efficiently. Although in many cases the probability of success for the test is close to 1, this test approac...

The Correlations of Farey Fractions

We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.

Multiplicative hyperring of fractions and coprime hyperideals

In this paper we will introduce the notion of coprime hyperideals in multiplicative hyperrings and we will show some properties of them. Then we introduce the notion of hyperring of fractions generated by a multiplicative hyperring and then we will show some properties of them.