Vol. 81, No. 1, 1979

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Resolution of sign ambiguities in Jacobi and Jacobsthal sums

Ronald James Evans

Vol. 81 (1979), No. 1, 71–80
Abstract

Let p be a prime 1 (mod 16). We obtain extensions of known congruences involving parameters of bioctic Jacobi sums (mod p). These extensions are used to give an elementary proof of an important congruence of Hasse relating parameters of quartic and octic Jacobi sums (mod p). This proof leads directly to an elementary resolution of sign ambiguities of parameters of certain quartic, octic, and bioctic Jacobi and Jacobsthal sums. E. Lehmer’s work on ambiguities in quartic sums is thereby extended.

Mathematical Subject Classification
Primary: 10G05, 10G05
Milestones
Received: 5 April 1978
Revised: 10 July 1978
Published: 1 March 1979
Authors
Ronald James Evans