On the coefficients of Jacobi sums

in prime cyclotomic fields

Author:
F. Thaine

Journal:
Trans. Amer. Math. Soc. **351** (1999), 4769-4790

MSC (1991):
Primary 11R18; Secondary 11T22

DOI:
https://doi.org/10.1090/S0002-9947-99-02223-0

Published electronically:
July 1, 1999

MathSciNet review:
1475696

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be prime numbers, and let be a primitive root mod . For , denote by the Jacobi sum . We study the integers such that and . We give a list of properties that characterize these coefficients. Then we show some of their applications to the study of the arithmetic of , in particular to the study of Vandiver's conjecture. For , let be the number of distinct roots of in . We show that . We give closed formulas for the numbers and in terms of quadratic and cubic power residue symbols mod .

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Additional Information

**F. Thaine**

Affiliation:
Department of Mathematics and Statistics - CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, H3G 1M8, Canada

Email:
ftha@vax2.concordia.ca

DOI:
https://doi.org/10.1090/S0002-9947-99-02223-0

Received by editor(s):
May 8, 1997

Received by editor(s) in revised form:
August 29, 1997

Published electronically:
July 1, 1999

Additional Notes:
This work was supported in part by grants from NSERC and FCAR

Article copyright:
© Copyright 1999
American Mathematical Society