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Anderson-Stark units for $ {\mathbb{F}}_{q}[\theta]$


Authors: Bruno Anglès, Federico Pellarin and Floric Tavares Ribeiro
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11R58, 11M38; Secondary 11G09
DOI: https://doi.org/10.1090/tran/6994
Published electronically: August 15, 2017
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Abstract: We investigate the arithmetic of special values of a new class of $ L$-functions recently introduced by the second author. We prove that these special values are encoded in some particular polynomials which we call Anderson-Stark units. We then use these Anderson-Stark units to prove that $ L$-functions can be expressed as sums of polylogarithms.


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Bruno Anglès
Affiliation: Normandie Université, Université de Caen Normandie, CNRS UMR 6139, Campus II, Boulevard Maréchal Juin, B.P. 5186, 14032 Caen Cedex, France
Email: bruno.angles@unicaen.fr

Federico Pellarin
Affiliation: Institut Camille Jordan, UMR 5208, Site de Saint-Etienne, 23 rue du Dr. P. Michelon, 42023 Saint-Etienne, France
Email: federico.pellarin@univ-st-etienne.fr

Floric Tavares Ribeiro
Affiliation: Normandie Université, Université de Caen Normandie, CNRS UMR 6139, Campus II, Boulevard Maréchal Juin, B.P. 5186, 14032 Caen Cedex, France
Email: floric.tavares-ribeiro@unicaen.fr

DOI: https://doi.org/10.1090/tran/6994
Received by editor(s): January 27, 2015
Received by editor(s) in revised form: May 20, 2016
Published electronically: August 15, 2017
Additional Notes: The second author was supported by the ANR HAMOT
Article copyright: © Copyright 2017 American Mathematical Society