On a construction of C 1 ( p ) functionals from p -extensions of algebraic number fields
Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 29-50.

Soit k un corps de nombres et k /k une p -extension. Nous construisons un p T-1-morphisme naturel de lim k n × p dans un sous-ensemble particulier de C 1 ( p ) * , le dual de l’espace vectoriel sur p des fonctions continûment dérivables de p p . Nous appliquons les résultats au problème d’interpolation des sommes de Gauss attachées aux caractères de Dirichlet.

Let k be any number field, and let k /k be any p -extension. We construct a natural p T-1-morphism from lim k n × p into a special subset of C 1 ( p ) * , the dual of the p -vector space of continuously differentiable functions from p p . We apply the results to the problem of interpolating Gauss sums attached to Dirichlet characters.

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DOI : https://doi.org/10.5802/jtnb.968
Classification : 11R23
Mots clés : distributions, L-functions, Gauss sums, class group
@article{JTNB_2017__29_1_29_0,
     author = {Timothy All and Bradley Waller},
     title = {On a construction of $C^1(\mathbb{Z}_p)$ functionals from $\mathbb{Z}_p$-extensions of algebraic number fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {29--50},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {1},
     year = {2017},
     doi = {10.5802/jtnb.968},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.968/}
}
Timothy All; Bradley Waller. On a construction of $C^1(\mathbb{Z}_p)$ functionals from $\mathbb{Z}_p$-extensions of algebraic number fields. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 29-50. doi : 10.5802/jtnb.968. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.968/

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