Effective Ratner theorem for SL(2,R)⋉R2 and gaps in n modulo 1

DOI10.1112/jlms/jdw025zbMath1368.37008arXiv1311.6387OpenAlexW2403930749MaRDI QIDQ2822139

Ilya Vinogradov, Timothy D. Browning

Publication date: 27 September 2016

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6387

zbMATH Keywords

exponential sumhorocycle flow

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Ergodicity, mixing, rates of mixing (37A25) Distribution modulo one (11J71) Homogeneous flows (37A17)

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Exponential multiple mixing for some partially hyperbolic flows on products of \(\mathrm{PSL}(2, \mathbb{R})\) ⋮ Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7--12, 2023 ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ An effective equidistribution result for SL(2,R)⋉(R2)⊕k and application to inhomogeneous quadratic forms ⋮ Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions ⋮ An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\)

Cites Work

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• Logarithm laws for unipotent flows. I.
• An effective Ratner equidistribution result for SL\((2,\mathbb R)\ltimes \mathbb R^2\)
• Statistics of gaps in the sequence {√𝑛}
• Random Affine Lattices
• Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series
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• The Distribution of Directions in an Affine Lattice: Two-Point Correlations and Mixed Moments
• The two-point correlation function of the fractional parts of $\sqrt {n}$ is Poisson
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• On Exponential Sums in Finite Fields

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