Niclas Technau

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20162024

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14 papers · 1 filter

math.NT2022

Counting multiplicative approximations

Sam Chow, Niclas Technau

A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals of the same denominator, multiplying the errors. In a lesser-known paper, Wang and…

math.NT2021

The metric theory of the pair correlation function for small non-integer powers

Zeév Rudnick, Niclas Technau

For $0 < θ < 1$ , we show that for almost all $α$ , the pair correlation function of the sequence of fractional parts of ${α n^{θ} : n \geq 1}$ is Poissonian.

math.NT2020

Lehmer without Bogomolov

Fabien Pazuki, Niclas Technau, Martin Widmer

We construct fields of algebraic numbers that have the Lehmer property but not the Bogomolov property. This answers a recent implicit question of Pengo and the first author.

math.NT2020

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 $α > 1$ , the fractional parts of the geometric progression $(α^{n})_{n \geq 1}$ are equidistributed mo…

math.NT2020

On the correlations of $n^{α}$ 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 ${n^{α}}$ of the sequence $(n^α)_{n\ge1…

math.NT2020

On the triple correlations of fractional parts of $n^{2} α$

Niclas Technau, Aled Walker

For fixed $α \in [0, 1]$ , consider the set $S_{α, N}$ of dilated squares $α, 4 α, 9 α, \dots, N^{2} α$ modulo $1$ . Rudnick and Sarnak conjectured that for Lebesgue almost all such $α$ t…

Counting multiplicative approximations

The metric theory of the pair correlation function for small non-integer powers

Lehmer without Bogomolov

Gap statistics and higher correlations for geometric progressions modulo one

On the correlations of nα mod 1

On the triple correlations of fractional parts of n2α

On the correlations of $n^{α}$ mod 1

On the triple correlations of fractional parts of $n^{2} α$