In
mathematics, Jacobsthal sums are finite sums of
Legendre symbols related to
Gauss sum
In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically
:G(\chi) := G(\chi, \psi)= \sum \chi(r)\cdot \psi(r)
where the sum is over elements of some finite commutative ring , is a ...
s. They were introduced by .
Definition
The Jacobsthal sum is given by
:
where ''p'' is prime and () is the
Legendre symbol.
References
*
*
Further reading
* {{citation , last=Storer , first=Thomas , title=Cyclotomy and difference sets , location=Chicago , publisher=Markham Publishing Company , year=1967 , zbl=0157.03301
Number theory