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The Jacobi sums of order twenty-two


Author: Yun-cheng Zee
Journal: Proc. Amer. Math. Soc. 28 (1971), 25-31
MSC: Primary 10.66
DOI: https://doi.org/10.1090/S0002-9939-1971-0272748-5
MathSciNet review: 0272748
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Abstract: This paper completes the analysis of the Jacobi sums of order 22 outlined by L. E. Dickson. Furthermore, it is shown that a prime $ p$ of the form $ 22f + 1$ has the binary quadratic decomposition $ 4p = {u^2} + 11{v^2}$ and that certain Jacobi sums can be evaluated in terms of $ u$ and $ v$, where $ u$ satisfies $ u \equiv 9\pmod 11$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0272748-5
Keywords: Cyclotomy, cyclotomic field, Jacobi sum, reduced Jacobi sum, conjugate, cyclotomic number, Gaussian sum, Davenport and Hasse identity, Dickson-Hurwitz sum, binary quadratic decomposition
Article copyright: © Copyright 1971 American Mathematical Society

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