On the statistics of pairs of logarithms of integers
Parkkonen, J., & Paulin, F. (2022). On the statistics of pairs of logarithms of integers. Moscow journal of combinatorics and number theory, 11(4), 335-372. https://doi.org/10.2140/moscow.2022.11.335
Published in
Moscow journal of combinatorics and number theoryDate
2022Discipline
Analyysin ja dynamiikan tutkimuksen huippuyksikköMatematiikkaAnalysis and Dynamics Research (Centre of Excellence)MathematicsCopyright
© Mathematical Sciences Publishers
We study the statistics of pairs of logarithms of positive integers at various scalings, either with trivial weights or with weights given by the Euler function, proving the existence of pair correlation functions. We prove that at the linear scaling, which is not the usual scaling by the inverse of the average gap, the pair correlations exhibit a level repulsion similar to radial distribution functions of fluids. We prove total loss of mass phenomena at superlinear scalings, and constant nonzero asymptotic behavior 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 PSL2(Z)∖H2R.
Publisher
Mathematical Sciences PublishersISSN Search the Publication Forum
2220-5438Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/160421677
Metadata
Show full item recordCollections
License
Related items
Showing items with similar title or keywords.
-
Logarithmic mean inequality for generalized trigonometric and hyperbolic functions
Bhayo, Barkat; Yin, Li (Editura Scientia; Universitatea Sapientia Cluj-Napoca, 2015)In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean. -
Model nuclear energy density functionals derived from ab initio calculations
Salvioni, G.; Dobaczewski, J.; Barbieri, C.; Carlsson, G.; Idini, A.; Pastore, A. (Institute of Physics, 2020)We present the first application of a new approach, proposed in (2016J.Phys.G:Nucl.Part.Phys.4304LT01) to derive coupling constants of the Skyrme energy density functional (EDF) fromab initioHamiltonian. By perturbing theab ... -
On Limits at Infinity of Weighted Sobolev Functions
Eriksson-Bique, Sylvester; Koskela, Pekka; Nguyen, Khanh (Elsevier, 2022)We study necessary and sufficient conditions for a Muckenhoupt weight w∈Lloc1(Rd) that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions u∈Wloc1,p(Rd,w) with a p-integrable ... -
Existence and uniqueness of ρ(x)-harmonic functions for bounded and unbounded ρ(x)
Keisala, Jukka (University of Jyväskylä, 2011) -
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
Repin, Sergey (Springer, 2019)We consider inequalities of the Poincaré–Steklov type for subspaces of H1 -functions defined in a bounded domain Ω∈Rd with Lipschitz boundary ∂Ω . For scalar valued functions, the subspaces are defined by zero mean ...