54 citations · 504 across the 52 of their papers we have counts for
22 papers · 1 filter
Square roots and lattices
Jens Marklof
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of and directional statistics f…
Bounds for theta sums in higher rank II
Jens Marklof, Matthew Welsh
In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a l…
Poissonian pair correlation for directions in multi-dimensional affine lattices, and escape of mass estimates for embedded horospheres
Wooyeon Kim, Jens Marklof
We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermor…
Fine-scale distribution of roots of quadratic congruences
Jens Marklof, Matthew Welsh
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence , with square-free and $D\not\equiv 1 \bmod 4…
A five distance theorem for Kronecker sequences
Alan Haynes, Jens Marklof
The three distance theorem (also known as the three gap theorem or Steinhaus problem) states that, for any given real number and integer , there are at most three values for…
Delone sets generated by square roots
Jens Marklof
Delone sets are locally finite point sets, such that (a) any two points are separated by a given minimum distance, and (b) there is a given radius so that every ball of that radius…