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math.NT2013
The two-point correlation function of the fractional parts of \sqrt{n} is Poisson
Daniel El-Baz, Jens Marklof, Ilya Vinogradov
Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to inf…
math.NT2013
The distribution of directions in an affine lattice: two-point correlations and mixed moments
Daniel El-Baz, Jens Marklof, Ilya Vinogradov
We consider an affine Euclidean lattice and record the directions of all lattice vectors of length at most . Strömbergsson and the second author proved in [Annals of Math.~173 (…
math.NT2013
On a conjecture of Dekking : The sum of digits of even numbers
Iurie Boreico, Daniel El-Baz, Thomas Stoll
Let and denote by the sum-of-digits function in base . For consider $$# \{0 \le n < N : \;\;s_q(2n) \equiv j \pmod q \}.$$ In 1983, F. M. Dekking…