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1999 A problem concerning a character sum
Edlyn Teske, Hugh C. Williams
Experiment. Math. 8(1): 63-72 (1999).

Abstract

Let p be a prime congruent to -1 modulo 4, $\kron{n}{p}$ the Legendre symbol and $S(k) = \sum_{n=1}^{p-1}n^k \kron{n}{p}$. The problem of finding a prime p such that $S(3) >0$ was one of the motivating forces behind the development of several of Shanks' ideas for computing in algebraic number fields, although neither he nor D. H. and Emma Lehmer were ever successful in finding such a p. In this paper we exhibit some techniques which were successful in producing, for each k such that $3\le k \le 2000$, a value for p such that $S(k) >0$.

Citation

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Edlyn Teske. Hugh C. Williams. "A problem concerning a character sum." Experiment. Math. 8 (1) 63 - 72, 1999.

Information

Published: 1999
First available in Project Euclid: 12 March 2003

zbMATH: 0938.11061
MathSciNet: MR1685038

Subjects:
Primary: 11L40
Secondary: 11Y35

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 1 • 1999
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