On the evaluation of Brewer’s character sums
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- by Reinaldo E. Giudici, Joseph B. Muskat and Stanley F. Robinson PDF
- Trans. Amer. Math. Soc. 171 (1972), 317-347 Request permission
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 \[ \sum \limits _{x = 1}^p {{}_\chi ({V_n}(x,1))}, \] $\chi$ 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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- 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