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arXiv · 2401.12618

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

Xavier Caruso·Quentin Gazda
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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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Xavier Caruso, Quentin Gazda. 2024-01-23. Computation of classical and $v$-adic $L$-series of $t$-motives. https://doi.org/10.1007/s40993-024-00588-5

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