5 citations · 9 across the 5 of their papers we have counts for
5 papers
Multiple Legendre polynomials in Diophantine approximation
Raffaele Marcovecchio
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…
Vectors of type II Hermite-Padé approximations and a new linear independence criterion
Raffaele Marcovecchio
We propose a linear independence criterion, and outline an application of it. Down to its simplest case, it aims at solving this problem: given three real numbers, typically as spe…
Hypergeometric rational approximations to
Raffaele Marcovecchio, Wadim Zudilin
We give a new hypergeometric construction of rational approximations to , which absorbs the earlier one from 2003 based on Bailey's hypergeometric integrals. With t…
A classical functional generalization of the first Barnes lemma
Raffaele Marcovecchio
We give a brief account and a simpler proof of a contour integral formula for the Gauss hypergeometric function. Such formula is alternative to Barnes's integral formula and genera…
Some remarks in elementary prime number theory
Raffaele Marcovecchio
We give an outline of a generalization of the Gelfond-Schnirelmann method in elementary number theory. It is related to an integral of Selberg (1944) generalizing the Euler beta in…