On the evaluation of Brewer’s character sums

Giudici, Reinaldo E.; Muskat, Joseph B.; Robinson, Stanley F.

doi:10.1090/S0002-9947-1972-0306122-5

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
DOI: https://doi.org/10.1090/S0002-9947-1972-0306122-5
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 and 5 evaluated

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

$\chi$ the nonprincipal quadratic character of the prime

, 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 . Relevant quadratic decompositions of primes are studied.

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