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October 10, 2025Open Access

Arithmetic holonomy bounds and effective Diophantine approximation

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Authors

FCFrank CalegariNorthwestern UniversityVDVesselin DimitrovGeorgia Institute of TechnologyYTYunqing TangPrinceton University

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Implication

Research explores arithmetic holonomy bounds to derive effective irrationality measures, suggesting new approaches in Diophantine approximation.

Key Points

  • New methods for effective diophantine approximation yield effective measures of irrationality and linear independence.
  • Application of arithmetic holonomy bounds allowed derivation of classical effective Diophantine theorems, including results on the S-unit equation.
  • The research applies Dirichlet approximation techniques to produce irrationality measures for specific algebraic numbers, enhancing classical results.
  • A new proof of the transcendence of π is provided, highlighting applications of the proposed methodology.

Cite This Study

Calegari et al. (2025) studied this question.

synapsesocial.com/papers/68e90f526476c097794aa451https://doi.org/10.48550/arxiv.2510.04156
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