zetak

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

I've just noticed that zetak gives bogus results in moderately high accuracy:

  (19:04) gp > \p300
  (19:04) gp > precision( zetak(zetakinit(x^2-2),2.5), 28 )
  %1 = 7.291915302409519060840727684 E182

  (19:05) gp > \p28
  (19:05) gp > zetak(zetakinit(x^2-2),2.5)
  %2 = 1.243482357570925192192537147

I don't see anything obvious like a stack corruption. It looks like a problem
with the algorithm (coeff explosion + instability). Should be rewritten from
scratch I'm afraid...

The routine is already quite unable to handle inputs very close to integers,
for obvious reasons this time (using the functional equation and trying to
compute gamma values, with much less accurate output than apparently expected)

  (19:05) gp > \p28
  (19:05) gp > zetak(zetakinit(x^2-2), 2 - 1e-80)
  ***   division by zero in gdiv, gdivgs or ginv

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]