#16883: Modular forms for the theta subgroup (as part of Hecke triangle groups)
-------------------------------------+-------------------------------------
Reporter: jj | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.4
Component: modular forms | Resolution:
Keywords: theta subgroup | Merged in:
modular forms hecke triangle | Reviewers:
Authors: Jonas Jermann | Work issues:
Report Upstream: N/A | Commit:
Branch: u/jj/theta_group | 13ea3d8ecceea61173b0a8308ccafabe2769b208
Dependencies: #16839 | Stopgaps:
-------------------------------------+-------------------------------------
Description changed by jj:
Old description:
> Complete support for modular forms for the Hecke triangle group
> corresponding to n=infinity
> (the theta subgroup) with corresponding + further doctests/documentation.
>
> The situation is slightly different since there are now two cusps with
> two corresponding generators.
>
> In particular the limit of the generator f_rho tends to 1 and the
> generator
> for n=infinity is instead E4 which is the limit of f_rho^n.
>
> Note that only functions which are meromorphic and meromorphic at the
> cusps are considerd.
> E.g. E4 is the 8th power of theta, but smaller powers are no longer
> meromorphic at -1.
> Also note that limits of functions/coefficients as n tends to infinity
> are usually given by
> the corresponding function in the theta subgroup.
>
> Additionally the ticket adds support for experimental rationalization of
> series
> and a refactoring of code which in particular provides more robust
> numerical
> Fourier expansions.
>
> The ticket also fixes a mistake from #16839 and has some other small
> changes.
New description:
Complete support for modular forms for the Hecke triangle group
corresponding to n=infinity
(the theta subgroup) with corresponding + further doctests/documentation.
The situation is slightly different since there are now two cusps with
two corresponding generators.
In particular the limit of the generator f_rho tends to 1 and the
generator
for n=infinity is instead E4 which is the limit of f_rho^n.
Note that only functions which are meromorphic and meromorphic at the
cusps are considerd.
E.g. E4 is the 8th power of theta, but smaller powers are no longer
meromorphic at -1.
Also note that limits of functions/coefficients as n tends to infinity are
usually given by
the corresponding function in the theta subgroup.
Additionally the ticket adds support for experimental rationalization of
series,
refactoring of code which in particular provides more robust numerical
Fourier expansions
and Eisenstein series of arbitrary weight for n=3,4,6.
The ticket also fixes a mistake from #16839 and has some other small
changes.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/16883#comment:14>
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.
