#16477: implement Dirichlet series
-------------------------------------+-------------------------------------
Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-wishlist
Component: number theory | Resolution:
Keywords: moebius, zeta, | Merged in:
sigma, euler_phi, euler | Reviewers:
Authors: Jonathan Hanke, | Work issues: use pari, g.f. input
Ralf Stephan | Commit:
Report Upstream: N/A | 949082ca407de7df7ae2ce31ecfad4f5d21f3ffa
Branch: public/dirichlet- | Stopgaps:
series |
Dependencies: #18038, #18041 |
-------------------------------------+-------------------------------------
Comment (by rws):
Replying to [comment:24 jj]:
> {{{
> f = DirichletSeries(id)*DirichletSeries(id)
> f == DirichletSeries(sigma0)
> f[91234154]
> f // nice representations:
> => sum_{n in Z} (sum_{d|n} 1)
> or: sum_{n in Z} sigma0(n)
> }}}
> nice representations/output of coefficient functions after operations
(hard),
That would first need conversion of the g.f. into divisor sum form.
Another ticket.
> {{{
> id = ArithmeticFunctions().id()
> sigma0 = ArithmeticFunction(lambda n: sigma0(n))
> id*id == sigma0 // Dirichlet convolution
> }}}
That would need ability to compute a g.f. from the coefficients. I think
this is possible but hard.
> support functions from ideals (TODO: figure out the correct category for
the domain
> of coefficient functions).
And a third ticket.
So this ticket would prepare for the others by providing creation from
expressions of a limited form (polynomial fractions with generator from
`zeta(a*s+b)` and `L(c)`).
--
Ticket URL: <http://trac.sagemath.org/ticket/16477#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
