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A reciprocity law in function fields

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Abstract

We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.

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Acknowledgements

The author would like to thank the anonymous referee for the careful reading and insightful comments that improved this paper. This work was supported by JSPS KAKENHI Grant Number 21K03192.

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  1. Department of Applied Mathematics, Okayama University of Science, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yoshinori Hamahata

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  1. Yoshinori Hamahata
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Correspondence to Yoshinori Hamahata.

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Hamahata, Y. A reciprocity law in function fields. Arch. Math. (2024). https://doi.org/10.1007/s00013-024-02006-9

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  • DOI: https://doi.org/10.1007/s00013-024-02006-9

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