On the evaluation of Brewer’s character sums
| Autor: | Reinaldo E. Giudici, Stanley F. Robinson, Joseph B. Muskat |
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| Rok vydání: | 1972 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 171:317-347 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1972-0306122-5 |
| Popis: | A decade ago in this journal B. W. Brewer defined a sequence of polynomials V n ( x , 1 ) {V_n}(x,1) and for n = 4 n = 4 and 5 evaluated \[ ∑ x = 1 p χ ( V n ( x , 1 ) ) , \sum \limits _{x = 1}^p {{}_\chi ({V_n}(x,1))}, \] χ \chi the nonprincipal quadratic character of the prime p p , in closed form. A. L Whiteman derived these results by means of cyclotomy. Brewer subsequently defined V n ( x , Q ) {V_n}(x,Q) . This paper applies cyclotomy to the more general polynomials and provides evaluations for several more values of n n . Relevant quadratic decompositions of primes are studied. |
| Databáze: | OpenAIRE |
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