Special L-values of t-motives: a conjecture

Abstract

We propose a conjecture on special values of $L$-functions in a function field context with positive characteristic coefficients. For $M$ a uniformizable $t$-motive with everywhere good reduction we conjecture a relation between the value of the Goss $L$-function $L(M^{\vee },s)$ at $s=0$ and the uniformization of the abelian $t$-module associated with $M$. When $M$ is a power of the Carlitz $t$-motive the conjecture specializes to a theorem of Anderson and Thakur on Carlitz zeta values. Beyond this case we present numerical evidence.

in International Mathematics Research Notices (2009)

References in corpus (1)

• Artin t-Motifs

Cited by in corpus (5)

• A Dirichlet unit theorem for Drinfeld modules
• Log-algebraic identities on Drinfeld modules and special L-values
• Special values of Goss $L$-series attached to Drinfeld modules of rank 2
• Algorithms for computing norms and characteristic polynomials on general Drinfeld modules
• On the transcendence of special values of Goss $L$-functions attached to Drinfeld modules