On Lara Rodr\'iguez' full conjecture for double zeta values in function fields

Abstract

This paper discusses four formulae conjectured by J. A. Lara Rodr\'iguez on certain power series in function fields, which yield a 'harmonic product' formula for Thakur's double zeta values. We prove affirmatively the first two formulae. While we detect and correct errors in the last two formulae, and prove the corrected ones.