Year: 2014
Type: article
Abstract: 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.
Author: Raffaele Marcovecchio
Institution: University of Pisa
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2048620162