Jacobsthal sum
Appearance
In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by Jacobsthal (1907).
Definition
The Jacobsthal sum is given by
where p is prime and () is the Legendre symbol.
References
- Berndt, Bruce C.; Evans, Ronald J. (1979), "Sums of Gauss, Eisenstein, Jacobi, Jacobsthal, and Brewer", Illinois Journal of Mathematics, 23 (3): 374–437, ISSN 0019-2082, MR 0537798, Zbl 0393.12029[permanent dead link]
- Jacobsthal, E. (1907), "Über die Darstellung der Primzahlen der Form 4n + 1 als Summe zweier Quadrate", Journal für die reine und angewandte Mathematik: 238–245, ISSN 0075-4102, JFM 38.0238.03
Further reading
- Storer, Thomas (1967), Cyclotomy and difference sets, Chicago: Markham Publishing Company, Zbl 0157.03301