Large deviations from the circular law
Gérard Ben Arous, Ofer Zeitouni (1998)
ESAIM: Probability and Statistics
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Displaying similar documents to “Limit theorems for the number of maxima in random samples from planar regions.”
Large deviations from the circular law
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On differences of two squares
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The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).
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ESAIM: Control, Optimisation and Calculus of Variations
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