Xavier-François Roblot on Mon, 22 Dec 2008 19:57:49 +0100

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Re: Functions elllderiv and ellanalyticrank

Bill Allombert wrote:
On Sat, Dec 20, 2008 at 10:16:23AM +0100, Karim Belabas wrote:
* Bill Allombert [2008-12-19 23:20]:
On Fri, Dec 19, 2008 at 07:20:53PM +0100, Karim Belabas wrote:
2) I think elllderiv should be renamed ellL1 for consistency with bnrL1
(and maybe add a flag so that both functions have the same semantic).
Had forgotten to commit this one, sorry. No flag added: contrary to bnrL1, we
compute the value at the center of the critical strip, so no symmetry
in the special value here.

I'd like to clarify something:
Is it correct that bnrL1 returns L^(r)(0, chi)/r! and ellL1 returns L^(r)(1)?
The 1/r! missing factor is slighly inconsistent. However the functions
are already sufficiently differents so that it might not matter to much.

This is correct. Actually, we wanted the result of (the former) elllderiv to be consistent with its name and thus to return the value of the r-th derivative at s=1. If the name of the function is now ellL1, then it should definitely be modified so that it returns instead the coefficient of (s-1)^r in the Taylor expansion of the L-function at s=1. Note that we considered the name ellL1 at some point but decided not to use it to be consistent with elllserives (big 'L' vs small 'l').