On a construction of C 1 (ℤ p ) functionals from ℤ p -extensions of algebraic number fields
Timothy All1 ; Bradley Waller2
1 301 W. Wabash Ave Crawfordsville, IN 47933, USA
2 231 W. 18th Ave Columbus OH 43210, USA
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 ℤ p -extension. Nous construisons un ℤ p 〚T-1〛-morphisme naturel de lim ←k n × ⊗ ℤ ℤ p dans un sous-ensemble particulier de C 1 (ℤ p ) * , le dual de l’espace vectoriel sur ℂ p des fonctions continûment dérivables de ℤ p →ℂ 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 ℤ p -extension. We construct a natural ℤ p 〚T-1〛-morphism from lim ←k n × ⊗ ℤ ℤ p into a special subset of C 1 (ℤ p ) * , the dual of the ℂ p -vector space of continuously differentiable functions from ℤ p →ℂ p . We apply the results to the problem of interpolating Gauss sums attached to Dirichlet characters.

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

1 301 W. Wabash Ave Crawfordsville, IN 47933, USA
2 231 W. 18th Ave Columbus OH 43210, USA
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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/

[1] Timothy All On p-adic annihilators of real ideal classes, J. Number Theory, Volume 133 (2013) no. 7, pp. 2324-2338 | DOI

[2] Yvette Amice Duals, Proceedings of the Conference on p-adic Analysis (Nijmegen, 1978) (Report), Volume 7806 (1978), pp. 1-15

[3] Catalin Barbacioru A Generalization of Volkenborn Integral, The Ohio State University, USA (2002) (Ph. D. Thesis)

[4] Keninchi Iwasawa On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, Volume 16 (1694), pp. 42-82 | DOI

[5] Keninchi Iwasawa On p-adic L-functions, Ann. of Math., Volume 89 (1969), pp. 198-205 | DOI

[6] Jonathan Lubin; John Tate Formal complex multiplication in local fields, Ann. of Math., Volume 81 (1965), pp. 380-387 | DOI

[7] Jürgen Neukirch Algebraic number theory, Grundlehren der Mathematischen Wissenschaften, 322, Springer-Verlag, Berlin, 1999 (Translated from the 1992 German original)

[8] Alain M. Robert A course in p-adic analysis, Graduate Texts in Mathematics, 198, Springer-Verlag, New York, 2000

[9] W. Sinnott On the Stickelberger ideal and the circular units of an abelian field, Invent. Math., Volume 62 (1980/81) no. 2, pp. 181-234 | DOI

[10] Lawrence C. Washington Introduction to cyclotomic fields, Graduate Texts in Mathematics, 83, Springer-Verlag, New York, 1997

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