F. Boca

activity

19992004

most citedThe correlations of Farey fractions

1 citations · 1 across the 3 of their papers we have counts for

collaborators

8 papers

math.NT2004

On the correlations of directions in the Euclidean plane

Florin P. Boca, Alexandru Zaharescu

We study the correlations of directions $P_{0} P$ in the Euclidean plane, where $P_{0}$ is a point in a fixed disc, $P$ is an integer lattice point in the square $[- Q, Q]^{2}$ , and $Q\to…

math.NT2004★ 1 cited

The correlations of Farey fractions

Florin P. Boca, Alexandru Zaharescu

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

math.NT2003

The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit

Florin P. Boca, Alexandru Zaharescu

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof fo…

math-ph2002

Norm estimates of almost Mathieu operators

Florin P. Boca, Alexandru Zaharescu

We estimate the norm of the almost Mathieu operator $H_{θ, λ} = U + U^{*} + (λ /2) (V + V^{*})$ in the rotation $C^{*}$ -algebra $A_{θ} = C^{*} (U, V u ni t a r i es; U V = e^{2 π i θ} V U)$ . In this process, we signifi…

math.NT2002

On the distribution of the Farey sequence with odd denominators

F. P. Boca, C. Cobeli, A. Zaharescu

We prove some asymptotic results on the distribution of h-tuples of consecutive Farey fractions of order Q with odd denominators as $Q \to \infty$ .

math.NT2002

On the index of Farey sequences

F. P. Boca, R. N. Gologan, A. Zaharescu

We prove some asymptotic formulae concerning the distribution of the index of Farey fractions of order Q as $Q \to \infty$ .