sou nonyma on Wed, 16 May 2012 18:33:00 +0200

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 Re: zetap

hello
so i am currently searching to have only zeta on 3-adic numbers
so with the formula i find that :
zetap(s)=2*zetahurwitz(s,1/3)/p
but i don't get the same answer as sage
is this because of the formula?

2012/5/15 Bill Allombert
On Tue, May 15, 2012 at 09:02:12PM +0200, sou nonyma wrote:
> i think i tell ou the wrong function
> i want to find the kubota leopold zeta function , but if i apply the
> formula of L function to the trivial character,
> i find that it equals the hurwitz zeta function at x=0
> but in the definition of the hurwitz zeta function a x^(-j) appear so i get
> a division by zero
>

Looking at the code, you have to take f=p and sum from 1 to p-1 in the formula,
i.e. (for odd p):

zetap(x) = 2*sum(a=1,(p-1)/2,zetah(s,a/p))/p

I am quite unable to explain you why this is so.

Cheers,
Bill.

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