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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11A15, 11L99

Retrieve articles in all journals with MSC: 11A15, 11L99

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society