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Transactions of the American Mathematical Society

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On Artin's conjecture: Linear slices of diagonal hypersurfaces


Authors: Jörg Brüdern and Olivier Robert
Journal: Trans. Amer. Math. Soc. 372 (2019), 1867-1911
MSC (2010): Primary 11E76, 11E95; Secondary 11D79
DOI: https://doi.org/10.1090/tran/7635
Published electronically: May 9, 2019
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Abstract: Artin's conjecture is established for all forms that can be realised as a diagonal form on a hyperplane.


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Jörg Brüdern
Affiliation: Universität Göttingen, Mathematisches Institut, Bunsenstr. 3–5, D 37073 Göttingen, Germany
Email: bruedern@uni-math.gwdg.de

Olivier Robert
Affiliation: Université de Lyon and Université de Saint-Etienne, Institut Camille Jordan CNRS UMR 5208, 23, rue du Dr P. Michelon, F-42000, Saint-Etienne, France
Email: olivier.robert@univ-st-etienne.fr

DOI: https://doi.org/10.1090/tran/7635
Keywords: Artin's conjecture, forms of higher degree
Received by editor(s): July 1, 2017
Received by editor(s) in revised form: June 2, 2018, and June 11, 2018
Published electronically: May 9, 2019
Additional Notes: The authors are grateful to their home institutions for support on the occasion of mutual visits during the period when this paper was conceived.
The first author acknowledges with gratitude support by Deutsche Forschungsgemeinschaft and Schweizer Nationalfond.
Article copyright: © Copyright 2019 American Mathematical Society