Jacobsthal sum
From HandWiki
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
- [math]\displaystyle{ \phi_n(a)=\sum_{m\bmod p}\left(\dfrac{m(m^n+a)}{p}\right) }[/math]
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, https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-23/issue-3/Sums-of-Gauss-Eisenstein-Jacobi-Jacobsthal-and-Brewer/10.1215/ijm/1256048104.full
- 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, http://www.digizeitschriften.de/dms/img/?PPN=GDZPPN002166402
Further reading
- Storer, Thomas (1967), Cyclotomy and difference sets, Chicago: Markham Publishing Company
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