On the irrationality measure function in average
Denis Shatskov
TL;DR
This paper investigates the asymptotic behavior of the integral of the irrationality measure function, providing insights into how well real numbers can be approximated by rationals on average.
Contribution
It introduces new asymptotic analysis for the integral of the irrationality measure function, advancing understanding of approximation properties of real numbers.
Findings
Derived asymptotic formulas for the integral of the irrationality measure function
Established bounds on the average irrationality measure
Enhanced understanding of Diophantine approximation on average
Abstract
We study asymptotics for the intergal of irrationality measure functions.
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Taxonomy
TopicsFuzzy Systems and Optimization · Optimization and Mathematical Programming · Mathematical and Theoretical Analysis