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- W4309965533 abstract "We study the correlations of pairs of logarithms of positive integers at various scalings, either with trivial weigths or with weights given by the Euler function, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations exhibit level repulsion, as it sometimes occurs in statistical physics. We prove total loss of mass phenomena at superlinear scalings, and Poissonian behaviour at sublinear scalings. The case of Euler weights has applications to the pair correlation of the lengths of common perpendicular geodesic arcs from the maximal Margulis cusp neighborhood to itself in the modular curve $operatorname{PSL}_2(mathbb Z)backslashmathbb H^2_{mathbb R}$." @default.
- W4309965533 created "2022-11-30" @default.
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- W4309965533 date "2022-11-25" @default.
- W4309965533 modified "2023-09-29" @default.
- W4309965533 title "On the statistics of pairs of logarithms of integers" @default.
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- W4309965533 doi "https://doi.org/10.2140/moscow.2022.11.335" @default.
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