Divisor Problems and the Pair Correlation for the Fractional Parts of n2

DOI10.1093/imrn/rnp239zbMath1211.11087arXiv0908.4389OpenAlexW2083769501MaRDI QIDQ4931139

Jimi L. Truelsen

Publication date: 4 October 2010

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4389

zbMATH Keywords

pair correlationdivisor functionfractional part

Mathematics Subject Classification ID

Distribution of integers with specified multiplicative constraints (11N25) Small fractional parts of polynomials and generalizations (11J54) Distribution modulo one (11J71)

Related Items (13)

Pair correlation for quadratic polynomials mod 1 ⋮ On exceptional sets in the metric Poissonian pair correlations problem ⋮ Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems ⋮ The variance of a restricted sum-of-squares function over short intervals in \(\mathbb{F}_q [t\)] ⋮ Modular hyperbolas ⋮ Gap statistics and higher correlations for geometric progressions modulo one ⋮ On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics ⋮ Correlations and distribution of essentially bounded functions in short intervals ⋮ On the restricted divisor function in arithmetic progressions ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ On the pair correlations of powers of real numbers ⋮ Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions ⋮ THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS

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