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From: Pubkeybreaker on 22 Mar 2010 10:07
On Mar 20, 5:03 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
wrote:
> 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.- Hide quoted text -
>
> - Show quoted text -

Please define e for us. What does *it* mean in Z/pZ?
From: Chip Eastham on 22 Mar 2010 10:46
On Mar 22, 10:07 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote:
> On Mar 20, 5:03 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
> wrote:
>
>
>
> > 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..- Hide quoted text -
>
> > - Show quoted text -
>
> Please define  e  for us.  What does *it* mean in   Z/pZ?

I could tell you, but when the series gets
to the term involving p!, the world and all
the finite field Fourier transforms inside
would blow [u]p!

--c
From: magya_bloom on 28 Mar 2010 19:33
On Mar 22, 7:07 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote:
> On Mar 20, 5:03 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
> wrote:
>
>
>
> > 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 theFouriertransform 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: TheFouriertransform....."
>
> > > --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..- Hide quoted text -
>
> > - Show quoted text -
>
> Please define  e  for us.  What does *it* mean in   Z/pZ?

e^(i*2*pi/p) is the p-th root of unity.
From: magya_bloom on 28 Mar 2010 19:34
On Mar 21, 2:08 pm, Timothy Murphy <gayle...(a)eircom.net> wrote:
> magya_bl...(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

x is also in Zp.
From: magya_bloom on 29 Mar 2010 13:57
On Mar 28, 4:34 pm, "magya_bl...(a)yahoo.com" <magya_bl...(a)yahoo.com>
wrote:
> On Mar 21, 2:08 pm, Timothy Murphy <gayle...(a)eircom.net> wrote:
>
> > magya_bl...(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
>
>  x is also in Zp.

Also, the fourier transform is the usual projection on the characters
of Zp (Fourier F(x) of f(x)):
F(x) = 1/sqrt(p) * sum_(j=0..p-1) f(j)*e^(i*2*pi*j*x/p)
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