A sharper multivariate Christol's theorem with applications to diagonals and Hadamard products
| hal.structure.identifier | Université Claude Bernard Lyon 1 [UCBL] | |
| dc.contributor.author | ADAMCZEWSKI, Boris | |
| hal.structure.identifier | Calcul formel, mathématiques expérimentales et interactions [MATHEXP] | |
| dc.contributor.author | BOSTAN, Alin | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | CARUSO, Xavier | |
| dc.date.accessioned | 2024-04-04T02:34:08Z | |
| dc.date.available | 2024-04-04T02:34:08Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190531 | |
| dc.description.abstractEn | We provide a new proof of the multivariate version of Christol's theorem about algebraic power series with coefficients in finite fields, as well as of its extension to perfect ground fields of positive characteristic obtained independently by Denef and Lipshitz, Sharif and Woodcok, and Harase. Our proof is elementary, effective, and allows for much sharper estimates. We discuss various applications of such estimates, in particular to a problem raised by Deligne concerning the algebraicity degree of reductions modulo p of diagonals of multivariate algebraic power series with integer coefficients. | |
| dc.description.sponsorship | Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007 | |
| dc.description.sponsorship | Décider l'irrationalité et la transcendance - ANR-19-CE40-0018 | |
| dc.language.iso | en | |
| dc.subject.en | Christol's theorem | |
| dc.subject.en | automatic sequences | |
| dc.subject.en | algebraic power series | |
| dc.subject.en | diagonals | |
| dc.subject.en | Hadamard products | |
| dc.title.en | A sharper multivariate Christol's theorem with applications to diagonals and Hadamard products | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Informatique [cs] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04116793 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04116793v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ADAMCZEWSKI,%20Boris&BOSTAN,%20Alin&CARUSO,%20Xavier&rft.genre=preprint |
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