Fast evaluation of some p-adic transcendental functions

We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect to the target precision and most of them are based on an adaptation to the-adic setting of the binary splitting and bit-burst strategies.Décider l'irrationalité et la transcendanceSûreté numérique pour les preuves assistées par ordinateurCorrespondance de Langlands p-adique : une approche constructive et algorithmiqu