$p$-adic logarithmic functions and applications

hirata @ math. cst.nihon-u.ac.jp AbStraCt We explain how we define $p$-adic logarithmic functions to provide a new lower bound for linear forms in two p-adic elliptic logarithms proven in [11]. We adapt the argument that relies on the interpolation method on the variable change introduced by G. Chudnovsky, and on Fa\‘a-di-Bruno $s$ formula adapted to matrices whose elements are p-adic elliptic logarithmic functions.