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Distribution of Lattice Points Visible from the Origin

- F. Boca, C. Cobeli, A. Zaharescu
- Mathematics
- 1 September 2000

Abstract:Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the origin and has a piecewise C1 boundary. For each integer Q≥ 1, we consider the integer lattice… Expand

On the structure of the irreducible polynomials over local fields

- N. Popescu, A. Zaharescu
- Mathematics
- 1 May 1995

The paper is concerned with the structure of irreducible polynomials in one variable over a local field (K, v). The main achievement is the definition of a system P(ƒ) of invariant factors for each… Expand

The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

- F. Boca, A. Zaharescu
- Mathematics
- 23 January 2003

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 for the existence of… Expand

The distribution of spacings between the fractional parts of n2α

- Z. Rudnick, P. Sarnak, A. Zaharescu
- Mathematics
- 17 February 2000

We study the distribution of normalized spacings between the fractional parts of an^2, n=1,2,.... We conjecture that if a is "badly approximable" by rationals, then the sequence of fractional parts… Expand

The distribution of spacings between fractional parts of lacunary sequences

- Z. Rudnick, A. Zaharescu
- Mathematics
- 13 December 1999

Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit… Expand

On the index of Farey sequences

- F. Boca, R. Gologan, A. Zaharescu
- Mathematics
- 7 January 2002

We prove some asymptotic formulae concerning the distri- bution of the index of Farey fractions of order Q as Q ! 1.

On the distribution of imaginary parts of zeros of the Riemann zeta function

- K. Ford, A. Zaharescu
- Mathematics
- 24 May 2004

Abstract We investigate the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta… Expand

Integrals of Eisenstein series and derivatives of L-functions

- S. Ahlgren, B. Berndt, A. Yee, A. Zaharescu
- Mathematics
- 2002

In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at… Expand

Explicit formulas for the pair correlation of zeros of functions in the Selberg class

- M. Murty, A. Zaharescu
- Mathematics
- 2002

For any two functions F and G in the Selberg class we prove explicit formulas which relate sums over pairs of zeros, of the form: P ÿTUgF ; gGUT f
rF rG to sums over prime powers, of the form: T… Expand

Continued fractions with three limit points

- G. Andrews, B. Berndt, J. Sohn, A. Yee, A. Zaharescu
- Mathematics
- 1 April 2005

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