The Quadratic Reciprocity Law by Zolotarev and its generalizations
https://doi.org/10.26907/2949-3919.2025.1.4-11
Abstract
In the paper of Duke and Hopkins (2005), following the approach of E.I. Zolotarev, an analogue of the quadratic reciprocity law for groups was obtained using the Kronecker symbol. We present a short proof of this statement using the Jacobi symbol. The work is mainly of a methodological nature. In this regard, we also provide a proof of the result established in the paper by Frobenius (1914), related to the combinatorial interpretation of the Jacobi symbol.
About the Author
A. N. Abyzov
Kazan Federal University
Russian Federation
Russian Federation
Adel Nailevich Abyzov
18 Kremlyovskaya str., Kazan 420008
References
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Review
For citations:
Abyzov A.N. The Quadratic Reciprocity Law by Zolotarev and its generalizations. Mathematics and Theoretical Computer Science. 2025;3(1):4-11. (In Russ.) https://doi.org/10.26907/2949-3919.2025.1.4-11
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