On a Quantitative Refinement of the Lagrange Spectrum
Julia Snyder2002, Acta Arithmetica
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Abstract
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This work explores a quantitative refinement of the Lagrange spectrum associated with irrational numbers. Building upon the foundational results established by Markoff and Hurwitz, the paper examines improved bounds for inequalities that describe the distribution of certain positive integers q relative to irrational numbers. The authors introduce a sequence of best possible constants related to the Lagrange spectrum and establish new results regarding the existence of multiple solutions to associated inequalities. The findings contribute to a deeper understanding of the relationships between irrational numbers and Diophantine approximations.
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