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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the evaluation of Brewer's character sums

Authors: Reinaldo E. Giudici, Joseph B. Muskat and Stanley F. Robinson
Journal: Trans. Amer. Math. Soc. 171 (1972), 317-347
MSC: Primary 10C20; Secondary 10G05
MathSciNet review: 0306122
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Abstract: A decade ago in this journal B. W. Brewer defined a sequence of polynomials $ {V_n}(x,1)$ and for $ n = 4$ and 5 evaluated

$\displaystyle \sum\limits_{x = 1}^p {{}_\chi ({V_n}(x,1))}, $

$ \chi$ the nonprincipal quadratic character of the prime $ p$, in closed form. A. L Whiteman derived these results by means of cyclotomy.

Brewer subsequently defined $ {V_n}(x,Q)$. This paper applies cyclotomy to the more general polynomials and provides evaluations for several more values of $ n$. Relevant quadratic decompositions of primes are studied.

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Article copyright: © Copyright 1972 American Mathematical Society

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