2025/12/15 by Marcovecchio, Raffaele
Mathematics · #Mathematical Dynamics and Fractals #Analytic Number Theory Research #Mathematical functions and polynomials
paper · doi:10.48550/arxiv.2512.12890
We construct a class of multiple Legendre polynomials and prove that they satisfy an Apéry-like recurrence. We give new upper bounds of the approximation measures of logarithms of rational numbers by algebraic numbers of bounded degree. We prove e.g. that the nonquadraticity exponent of log 2 is bounded from above by 12.841618..., thus improving upon a recent result of the author. Our construction also yields some other known results.