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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quintic reciprocity


Author: Charles Helou
Journal: Proc. Amer. Math. Soc. 117 (1993), 877-884
MSC: Primary 11A15; Secondary 11L99
MathSciNet review: 1155597
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Abstract: An expression for the rational inversion factor of the power residue symbol, of odd prime exponent $ n \equiv 1\;(\bmod \,4)$ (mod 4), is given. It is applied to the quintic case, where the resulting expression involves only a rational quadratic form representation of primes and the power residue character of Jacobi sums. A reciprocity relation for Jacobi sums is then deduced, for $ n = 5$, and conjectured to hold for all odd prime exponents $ n$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1155597-X
PII: S 0002-9939(1993)1155597-X
Article copyright: © Copyright 1993 American Mathematical Society