Resolution of Sign Ambiguities in Jacobi and Jacobsthal Sums
نویسنده
چکیده
Let p be a prime = 1 (mod 16). We obtain extensions of known congruences involving parameters of bioctic Jacobi sums (modp). These extensions are used to give an elementary proof of an important congruence of Ήasse 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.
منابع مشابه
Unambiguous Evaluations of Bidecic Jacobi and Jacobsthal Sums
For a class of primes p = 1 (mod 20) for which 2 is a quintic nonresidue, unambiguous evaluations of parameters of bidecic Jacobi and Jacobsthal sums (modp) are presented, in terms of the partition p = a + 5b+5c+5d, ab = d — c—cd. Similar results for sums of other orders have been obtained by E. Lehmer and by K. S. Williams. Subject classification (Amer. Math. Soc. (MOS) 1970): 10G05.
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