Niclas Technau

activity

20242026

collaborators

Showing math.NTShow all

6 papers · 1 filter

math.NT2026

Sharp Bounds for Rational Points Near Space Curves

Mingfeng Chen, Andreas Seeger, Rajula Srivastava +1

Let $Q \geq 1$ be large, and $δ \in (0, 1)$ be small. Denote by $C \subset R^{3}$ a sufficiently smooth curve with non-vanishing curvature and torsion. How many rational…

math.NT2026

Poissonian correlations of $I^\pm n^{d}$ mod $1$

Chris Lutsko, Nick Rome, Niclas Technau

Let $x (n) := I^\pm n^{d} mod 1$ for integer $d > 1$ and non-zero real $I^\pm$ . We show that ${x (n)}_{n > 0}$ has Poissonian $ℓ$ -point correlations for almost all choices of $I^\pm$ when $d$ i…

math.NT2026

Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds

Sam Chow, Rajula Srivastava, Niclas Technau +1

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subs…

math.NT2025

Gap distribution of $n mod 1$ and the circle method

Maksym RadziwiÅÅ, Niclas Technau

The distribution of the properly renormalized gaps of $n mod 1$ with $n < N$ converges (when $N \to \infty$ ) to a non-standard limit distribution, as Elk…

math.NT2024

Smooth discrepancy and Littlewood's conjecture

Sam Chow, Niclas Technau

Given $I^\pm \in [0, 1]^{d}$ , we estimate the smooth discrepancy of the Kronecker sequence $(n I^\pm mod 1)_{n \geq 1}$ . We find that it can be smaller tha…

math.NT2024

Density of Rational Points Near Flat/Rough Hypersurfaces

Rajula Srivastava, Niclas Technau

For $n \geq 3$ , let $M \subseteq R^{n}$ be a compact hypersurface, parametrized by a homogeneous function of degree $d \in R_{> 1}$ , with non-vanishing curv…

Sharp Bounds for Rational Points Near Space Curves

Poissonian correlations of I^±nd mod 1

Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds

Gap distribution of n​mod1 and the circle method

Smooth discrepancy and Littlewood's conjecture

Density of Rational Points Near Flat/Rough Hypersurfaces

Poissonian correlations of $I^\pm n^{d}$ mod $1$

Gap distribution of $n mod 1$ and the circle method