11 papers
Gap statistics and higher correlations for geometric progressions modulo one
Christoph Aistleitner, Simon Baker, Niclas Technau +1
Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every , the fractional parts of the geometric progression are equidistributed mo…
On the correlations of mod 1
Niclas Technau, Nadav Yesha
A well known result in the theory of uniform distribution modulo one (which goes back to Fejér and Csillag) states that the fractional parts of the sequence $(n^α)_{n\ge1…
On the triple correlations of fractional parts of
Niclas Technau, Aled Walker
For fixed , consider the set of dilated squares modulo . Rudnick and Sarnak conjectured that for Lebesgue almost all such t…
The metric theory of the pair correlation function of real-valued lacunary sequences
Niclas Technau, Zeév Rudnick
Let be a positive, real-valued, lacunary sequence. This note shows that the pair correlation function of the fractional parts of the dilations i…
The discrepancy of with respect to certain probability measures
Niclas Technau, Agamemnon Zafeiropoulos
Let be a lacunary sequence of integers. We show that if is a probability measure on such that , then for -almost…
Higher-rank Bohr sets and multiplicative diophantine approximation
Sam Chow, Niclas Technau
Gallagher's theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem po…