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Determinations of Analogues of Gauss Sums and Other Trigonometric Sums
Matthias Beck, Bruce C. Berndt, O-Yeat Chan +1
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the…
On the distribution of imaginary parts of zeros of the Riemann zeta function
Kevin Ford, Alexandru Zaharescu
We investigate the distribution of the fractional parts of ag, where a is a fixed non-zero real number and g runs over the imaginary parts of the non-trivial zeros of the Riemann z…
On the correlations of directions in the Euclidean plane
Florin P. Boca, Alexandru Zaharescu
We study the correlations of directions in the Euclidean plane, where is a point in a fixed disc, is an integer lattice point in the square , and $Q\to…
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.
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…
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 .