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F. Adiceam

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Preprint Sep 2026

Rational Points near Monofractal Curves and the Strong Oscillation Principle

In their previous work devoted to the distribution of rational points near Brownian motion, the authors conjectured the existence of an \emph{oscillation principle} governing the asymptotic behavior of the number of rational points with bounded denomi\-nators near the graph of a monofractal curve. In this note, a weake...

F. Adiceam, V. Pavlenkov, E. Zorin · 0 citations
Preprint Aug 2026

Rational Points and Brownian Motion

Given a real-valued function $f$, let $\mathcal{N}_f(\delta, Q)$ be the number of rational points with denominators at most $Q\ge 1$ in the $(\delta/Q)$-tubular neighbourhood of the graph of the function $f$. A heuristic predicts that the number of such points grows like the area of the neighbourhood provided that $\de...

F. Adiceam, V. Pavlenkov, E. Zorin · 1 citation

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