Re: L-functions help

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Griffin, Trevor (grif1718@vandals.uidaho.edu) [2018-09-03 23:19]:
> I’m searching for a method by which I can convert Euler products to
> their associated dirichlet series. I attempted to use the “direuler”
> command, however the 3rd argument requires an expression of the Euler
> product. I only have the factors (and roughly 1 or 2 of the factors
> are missing). Is there a function in Pari that could deal with Euler
> factors instead of the expression of the Euler product?

direuler can. Here's a possibility:

  P = primes(100);
  F = Map();
  \\ For instance zeta(s+1); more generally a map attaching Euler
  \\ factors to a few primes [prime(10) = 29 is missing]
  for (i=1, #P, if (i != 10, mapput(F, P[i], 1 / (1 - P[i]*x))))

  \\ product of all known Euler factors 
  direuler(p = 2, 100, if (mapisdefined(F,p,&z), z, 1))

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
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