Jacobi sums and Grössencharacters
[Sommes de Jacobi et Grössencharacters]
Publications Mathématiques de Besançon - Algèbre et Théorie des Nombres (2018), pp. 111-122.

En 1952, Weil a publié un article dans lequel il donne une interprétation des sommes de Jacobi en terme de Hecke Grössencharacters de corps cyclotomiques. Nous décrivons une version explicite de cette interprétation en lien avec un travail précédent sur l’implantation algorithmique des Grössencharacters. Nous corrigeons à ce sujet quelques erreurs liées au root numbers. Nous expliquons également comment la méthode des sommes de Jacobi peut être utilisée pour comprendre le comportement de la ramification modérée des motifs hypergéométriques.

In 1952, Weil published a paper describing how to interpret Jacobi sums in terms of Hecke Grössencharacters of cyclotomic fields. We describe an explicit version of this, with reference to our previous work concerning algorithmic implementation of Grössencharacters. We correct various errors involving root numbers in the latter, and also indicate how Jacobi sum methods can be used to understand tame primes of hypergeometric motives.

Publié le :
DOI : https://doi.org/10.5802/pmb.25
@article{PMB_2018____111_0,
     author = {Mark Watkins},
     title = {Jacobi sums and Gr\"ossencharacters},
     journal = {Publications Math\'ematiques de Besan\c con - Alg\`ebre et Th\'eorie des Nombres},
     pages = {111--122},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2018},
     doi = {10.5802/pmb.25},
     language = {en},
     url = {https://pmb.centre-mersenne.org/item/PMB_2018____111_0/}
}
Watkins, Mark. Jacobi sums and Grössencharacters. Publications Mathématiques de Besançon - Algèbre et Théorie des Nombres (2018), pp. 111-122. doi : 10.5802/pmb.25. https://pmb.centre-mersenne.org/item/PMB_2018____111_0/

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