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

Xavier Caruso; Quentin Gazda

doi:10.1007/s40993-024-00588-5

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

Xavier Caruso
, Quentin Gazda

Centre national de la recherche scientifique

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We design an algorithm for computing the L-series associated to an Anderson t-motive, exhibiting quasilinear complexity with respect to the target precision. Based on experiments, we conjecture that, after renormalization by the local factor at v, the order of vanishing at T=1 of the v-adic L-series of a given Anderson t-motive does not depend on the finite place v.

Original language	English
Article number	35
Journal	Research in Number Theory
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s40993-024-00588-5
Publication status	Published - 1 Mar 2025

Keywords

Algorithms
Anderson motives
L-series

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10.1007/s40993-024-00588-5

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abstract = "We design an algorithm for computing the L-series associated to an Anderson t-motive, exhibiting quasilinear complexity with respect to the target precision. Based on experiments, we conjecture that, after renormalization by the local factor at v, the order of vanishing at T=1 of the v-adic L-series of a given Anderson t-motive does not depend on the finite place v.",

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KW - L-series

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

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Keywords

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