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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'Gauss sum'
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more general Gauss sum by Larry Hammick
Correction id: 2645
Filed on: 2003-09-23 23:31:07
Status: Accepted on 2003-10-18 15:17:19
Type: Addendum
Correction text:
Hi,
In the item GaussSum, I think it should mention that p is prime.
But also, even if n is composite but >0, the sum over k of
exp(2\pi k^2/n) (k=0 to n-1)
is known to be
(1+i)sqrt(p) if p=0 mod 4
sqrt(p) if p=1 mod 4
0 if p=2 mod 4
i*sqrt(p) if p=3 mod 4.
LH |
Comment from object owner djao:
> In the item GaussSum, I think it should mention that p is prime.
It can't hurt to mention it.
> But also, even if n is composite but >0 ...
Both Ireland & Rosen "A Classical Introduction to Modern Number Theory" and Dym & McKean "Fourier Series and Integrals" require p to be prime in their definition of Gauss sum. Accordingly, I think your fact belongs in another entry, and not in the "Gauss sum" entry. |
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