From Wikipedia, the free encyclopedia
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
- 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