sou nonyma on Fri, 18 May 2012 18:05:01 +0200

 Re: zetap

i found that i was not clear so here are few value of my algorithme:
in the formula:
zetap(4)=3+2*3^2+2*3^6+2*3^7+O(3^8)       (i have change a few things since i put the previous message)
<x>=<1/p>=1+O(3^8)
the conbination C(1-s,1) for exemple C(-3,1)= 2+2*3+2*3^2+2*3^3+2*3^4+2*3^5+2*3^6+2*3^7+O(3^8)
the bernoulli number 6 B(6)=2*3^-1+3^2+2*3^3+2*3^4+3^5+O(3^6)
and the term for k=1  which is =2*3^3+3^4+3^5+3^6+3^7+O(3^8)

2012/5/17 sou nonyma
yes in the previous formula p was 3
and in sage , when i search for p-adic 4 zeta(4) i get :2*3^-2 + 3 + 2*3^2 + 3^4 + 2*3^7 + 3^9 + 2*3^10 + 3^11 + 2*3^12 + 2*3^13 + 2*3^14 + 2*3^15 + 2*3^16 + O(3^17)
and whith my program i get:
3+2*3^2+2*3^7+1*3^8+2*3^9+1*3^10+O(3^11)

2012/5/16 sou nonyma
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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