Pad\'e approximations of a class of G-functions and some applications

TL;DR

This paper constructs explicit Padé approximations for a class of G-functions and applies them to establish lower bounds for p-adic linear forms and to analyze rational approximations of these functions in the real setting.

Contribution

It provides explicit Padé approximations for G-functions and uses them to derive new lower bounds and approximation results in both p-adic and real contexts.

Findings

Established Baker-type lower bounds for p-adic linear forms in G-functions.

Developed explicit Padé approximations of the second kind for a specific class of G-functions.

Analyzed restricted rational approximations of G-functions in the real case.

Abstract

We construct explicitly Pad\'e approximations of the second kind for a special class of G-functions. These are then applied to prove a Baker-type lower bound for linear forms in the p-adic values of these functions. Moreover, we consider restricted rational approximations of the values of these functions in the real case.