Computing L-functions of $ λ$-adic representations of global function fields
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915753319464960 |
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| author | Angdinata, David Kurniadi |
| author_facet | Angdinata, David Kurniadi |
| contents | The L-function $ L(ρ_λ, s) $ of an almost everywhere unramified $ λ$-adic representation $ ρ_λ$ of a global function field $ \mathbb{F}_q(C) $ is known to be a rational function in $ q^{-s} $ satisfying a functional equation up to some complex sign $ ε(ρ_λ) $. This paper presents a systematic framework to compute the coefficients of $ L(ρ_λ, s) $ and its sign $ ε(ρ_λ) $ with some explicit examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing L-functions of $ λ$-adic representations of global function fields Angdinata, David Kurniadi Number Theory 11Y40, 11R59, 11M38 (Primary) 11G40, 14G10, 11M41 (Secondary) The L-function $ L(ρ_λ, s) $ of an almost everywhere unramified $ λ$-adic representation $ ρ_λ$ of a global function field $ \mathbb{F}_q(C) $ is known to be a rational function in $ q^{-s} $ satisfying a functional equation up to some complex sign $ ε(ρ_λ) $. This paper presents a systematic framework to compute the coefficients of $ L(ρ_λ, s) $ and its sign $ ε(ρ_λ) $ with some explicit examples. |
| title | Computing L-functions of $ λ$-adic representations of global function fields |
| topic | Number Theory 11Y40, 11R59, 11M38 (Primary) 11G40, 14G10, 11M41 (Secondary) |
| url | https://arxiv.org/abs/2601.17766 |