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Preprints, Working Papers, ... Year : 2024

Computation of classical and $v$-adic $L$-series of $t$-motives

Abstract

We design an algorithm for computing the $L$-series associated to an Anderson $t$-motives, exhibiting quasilinear complexity with respect to the target precision. Based on experiments, we conjecture that the order of vanishing at $T=1$ of the $v$-adic $L$-series of a given Anderson $t$-motive with good reduction does not depend on the finite place $v$.
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hal-04410981 , version 1 (22-01-2024)

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Xavier Caruso, Quentin Gazda. Computation of classical and $v$-adic $L$-series of $t$-motives. 2024. ⟨hal-04410981⟩
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