Power residue character of jacobi sums

Charles Helou

doi:10.1006/jnth.1994.1085

Power residue character of jacobi sums

Charles Helou

Penn State Brandywine

Research output: Contribution to journal › Article › peer-review

Abstract

In two previous papers [Proc. Amer. Math. Soc.117 (1993), 877- 884], [J. Number Theory44 (1993), 214-221], a reciprocity relation for the power residue symbol of odd prime exponent, between Jacobi sums, was conjectured then proved. This is here extended to the case of an arbitrary exponent, as a consequence of an expression for the power residue character of a Jacobi sum, modulo a rational prime power, in terms of Fermat quotients.

Original language	English (US)
Pages (from-to)	107-117
Number of pages	11
Journal	Journal of Number Theory
Volume	49
Issue number	1
DOIs	https://doi.org/10.1006/jnth.1994.1085
State	Published - Oct 1994

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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abstract = "In two previous papers [Proc. Amer. Math. Soc.117 (1993), 877- 884], [J. Number Theory44 (1993), 214-221], a reciprocity relation for the power residue symbol of odd prime exponent, between Jacobi sums, was conjectured then proved. This is here extended to the case of an arbitrary exponent, as a consequence of an expression for the power residue character of a Jacobi sum, modulo a rational prime power, in terms of Fermat quotients.",

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