Special values of Goss $L$-series attached to Drinfeld modules of rank 2

Abstract

Inspired by the classical setting, Goss defined $L$-series attached to Drinfeld modules. In this paper, for a fixed choice of a power $q$ of a prime number and a given Drinfeld module $\varphi$ of rank 2 with a certain condition on its coefficients, we give explicit formulas for the values of Goss $L$-series attached to $\varphi$ at positive integers $n$ such that $2n+1\le q$ in terms of polylogarithms and coefficients of the logarithm series of $\varphi$.

35 pages. Final version to appear in Journal de Théorie des Nombres de Bordeaux

References in corpus (3)

• Shtuka cohomology and special values of Goss L-functions
• Log-algebraic identities on Drinfeld modules and special L-values
• Deformation of Multiple Zeta Values and Their Logarithmic Interpretation in Positive Characteristic