#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 | 3d46db2825c6e5364897613293fb482293a41dab
Dependencies: #16839 | Stopgaps:
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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.
> In particular theta**8=E4, but not smaller powers since then the function
> is not 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.
>
> 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.
The ticket also fixes a mistake from #16839 and has some other small
changes.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/16883#comment:7>
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