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From: magya_bloom on 20 Mar 2010 13:01
is the Fourier transform of a Gaussian function another Gaussian in
finite fields? Any relevant books containing that? thanks.
From: dvsarwate on 20 Mar 2010 14:06
On Mar 20, 12:01 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
wrote:
> is the Fourier transform of a Gaussian function another Gaussian in
> finite fields? Any relevant books containing that? thanks.

If you know (and are willing to share with us) the
definition of a Gaussian function in a finite field,
the answer will be immediately obvious, and will
be Yes or No, though I can never remember which
it is. I don't know of any books containing this
information specifically, though it looks like a great
homework problem that could be included in some:

"Prove or disprove: The Fourier transform....."

--Dilip Sarwate
From: magya_bloom on 20 Mar 2010 17:03
On Mar 20, 11:06 am, dvsarwate <dvsarw...(a)gmail.com> wrote:
> On Mar 20, 12:01 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
> wrote:
>
> > is the Fourier transform of a Gaussian function another Gaussian in
> > finite fields? Any relevant books containing that? thanks.
>
> If you know (and are willing to share with us) the
> definition of a Gaussian function in a finite field,
> the answer will be immediately obvious, and will
> be Yes or No, though I can never remember which
> it is.  I don't know of any books containing this
> information specifically, though it looks like a great
> homework problem that could be included in some:
>
> "Prove or disprove: The Fourier transform....."
>
> --Dilip Sarwate

assume the field is Zp (Z mod p, where p is a prime). Gaussian
definition:
f(x) = e^(i * (2 * pi)/p * k * (x-j)^2) , where k and j are in Zp.
From: Timothy Murphy on 21 Mar 2010 17:08
magya_bloom(a)yahoo.com wrote:

> assume the field is Zp (Z mod p, where p is a prime). Gaussian
> definition:
> f(x) = e^(i * (2 * pi)/p * k * (x-j)^2) , where k and j are in Zp.

What does x-j mean, if x is a real number and j is in Zp.


--
Timothy Murphy
e-mail: gayleard /at/ eircom.net
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
From: Axel Vogt on 21 Mar 2010 17:49
magya_bloom(a)yahoo.com wrote:
> is the Fourier transform of a Gaussian function another Gaussian in
> finite fields? Any relevant books containing that? thanks.

There is such stuff in arithmetic geometry (due to Deligne, I think)
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