On periods of the third kind for rank 2 Drinfeld module

Abstract

In analogy with the periods of abelian integrals of differentials of the third kind for an elliptic curve defined over a number field, we introduce a notion of periods of the third kind for a rank 2 Drinfeld \({\mathbb{F}_{q}[t]}\)-module ρ defined over an algebraic function field. In this paper we establish explicit formulae for these periods of the third kind for ρ. Combining with the main result in Chang and Papanikolas (J. Am. Math. Soc. 25:123–150, 2012), we show the algebraic independence of the periods of first, second and third kinds for ρ.