We prove that the maximal abelian extension tamely ramified at infinity of the rational function field over Fq is generated by the values at the points in the algebraic closure of Fq of the higher derivatives of the so-called Anderson and Thakur function ω. We deduce a similar property for the special values of the higher derivatives of a new kind of L-series introduced by the second author.
Universal Gauss-Thakur sums and L -series / Angl(`(e))s, Bruno; Pellarin, Federico. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 200:2(2014), pp. 653-669. [10.1007/s00222-014-0546-8]
Universal Gauss-Thakur sums and L -series
Federico Pellarin
2014
Abstract
We prove that the maximal abelian extension tamely ramified at infinity of the rational function field over Fq is generated by the values at the points in the algebraic closure of Fq of the higher derivatives of the so-called Anderson and Thakur function ω. We deduce a similar property for the special values of the higher derivatives of a new kind of L-series introduced by the second author.File allegati a questo prodotto
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