On the correlations of \(n^\alpha \bmod 1\)

DOI10.4171/jems/1281arXiv2006.16629OpenAlexW3039783200MaRDI QIDQ6056482

Niclas Technau, Nadav Yesha

Publication date: 30 October 2023

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

Full work available at URL: https://arxiv.org/abs/2006.16629

zbMATH Keywords

Poissonian pair correlationlocal statisticsuniform distribution modulo 1

Mathematics Subject Classification ID

General theory of distribution modulo (1) (11K06) Special sequences (11K31)

Cites Work

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• The pair correlation function of fractional parts of polynomials
• Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems
• Gaps in \(\sqrt{n}\bmod 1\) and ergodic theory
• The distribution of spacings between quadratic residues
• On the pair correlations of powers of real numbers
• The metric theory of the pair correlation function of real-valued lacunary sequences
• A pair correlation problem, and counting lattice points with the zeta function
• GCD sums and sum-product estimates
• On pair correlation and discrepancy
• On exceptional sets in the metric Poissonian pair correlations problem
• The distribution of spacings between fractional parts of lacunary sequences
• ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY
• THE PRIMES ARE NOT METRIC POISSONIAN
• THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS
• The two-point correlation function of the fractional parts of $\sqrt {n}$ is Poisson
• The distribution of spacings between the fractional parts of \(n^2\alpha\)
• The distribution of spacings of real‐valued lacunary sequences modulo one

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