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- Florin Boca, Radu Gologan
- 2002

For any two consecutive Farey fractions Î³i = ai/qi < Î³i+1 = ai+1/qi+1, one has ai+1qi âˆ’ aiqi+1 = 1 and qi + qi+1 > Q. Conversely, if q and q â€² are two coprime integers in {1, . . . , Q} with q + q >â€¦ (More)

- Florin Boca
- 1999

For each Î± âˆˆ (0, 1), AÎ± denotes the universal C -algebra generated by two unitaries u and v, which fulfill the commutation relation uv = evu. We consider the order four automorphism Ïƒ of AÎ± definedâ€¦ (More)

- Florin Boca
- 1999

and Ï†A is the endomorphism induced on C(XA) by the one-sided subshift of finite type ÏƒA (see [6]) defined by (ÏƒAx)k = xk+1, x = (xk)kâˆˆN âˆˆ XA. Therefore Ï†A can be regarded as a non-commutativeâ€¦ (More)

- Florin Boca
- 2008

To the Farey tessellation of the upper half-plane we associate an AF algebra A encoding the cutting sequences that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of A.â€¦ (More)

- Florin Boca
- 2008

Let R (Î½) (x,y),Q denote the repartition of the Î½-point correlation measure of the finite set of directions P(x,y)P , where P(x,y) is the fixed point (x, y) âˆˆ [0, 1) 2 and P is an integer latticeâ€¦ (More)

- Florin Boca, Radu Gologan
- 2008

Abstract. Let l > 2 be an integer. For each Îµ âˆˆ (0, 2 ) remove from R 2 the union of discs of radius Îµ centered at the integer lattice points (m, n), with m . n (mod l). Consider a point-likeâ€¦ (More)

- Florin Boca
- 2000

1. Introduction. The problem of understanding the distribution of fractional parts of polynomials has a long history. Weyl [19] proved that, for any polynomial f (x) = Î± d x d + Î± dâˆ’1 x dâˆ’1 + Â· Â· Â· +â€¦ (More)

- Florin Boca
- 2006

For every two points z0, z1 in the upper-half plane H, consider all elements Î³ in the principal congruence group Î“(N), acting on H by fractional linear transformations, such that the hyperbolicâ€¦ (More)

- Florin Boca, Radu Gologan
- 2003

We remove a small disc of radius Îµ > 0 from the flat torus T2 and consider a point-like particle that starts moving from the center of the disk with linear trajectory under angle Ï‰. Let Ï„ÌƒÎµ(Ï‰) denoteâ€¦ (More)

- Florin Boca
- 2006

Let Î¦(N) denote the number of products of matrices [ 1 1 0 1 ] and [ 1 0 1 1 ] of trace equal to N , and Î¨(N) = N n=3 Î¦(n) be the number of such products of trace at most N . We prove an asymptoticâ€¦ (More)