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

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.

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.

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Accepted:
Published online:
DOI: 10.5802/jtnb.968
Classification: 11R23
Keywords: distributions, $L$-functions, Gauss sums, class group
All, Timothy 1; Waller, Bradley 2

1 301 W. Wabash Ave Crawfordsville, IN 47933, USA
2 231 W. 18th Ave Columbus OH 43210, USA
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All, Timothy; Waller, Bradley. 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, Volume 29 (2017) no. 1, pp. 29-50. doi : 10.5802/jtnb.968. http://archive.numdam.org/articles/10.5802/jtnb.968/

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