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arXiv · 0811.4522

Special L-values of t-motives: a conjecture

Lenny Taelman
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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.

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Lenny Taelman. 2008-11-27. Special L-values of t-motives: a conjecture. https://doi.org/10.1093/imrn%2Frnp038

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