Seminars: S. David, On linear independence of special values of Lerch functions

SEMINARS


Seminar on Complex Analysis (Gonchar Seminar) November 15, 2021 17:30, Moscow, Online

On linear independence of special values of Lerch functions S. David Paris Sorbonne University
Abstract: We shall discuss a recent joint work with Makoto Kawashima and Noriko Hirata-Kohno. For any set of algebraic numbers in a fixed number field $K$ satisfying standard metric conditions in the theory (close enough to zero), we prove that the values of Lerch functions with freely chosen shifts are linearly independent over $K$. This is done via a construction of an explicit system of Padé approximation. As a special case, we recover our previous results on polylogarithms. Language: English Website: https://mi-ras-ru.zoom.us/j/6119310351?pwd=anpleGlnYVFXNEJnemRYZk5kMWNiQT09 ^* ID: 611 931 0351. Password: 5MAVBP