At the moment very little functionality is implemented – this is mostly a placeholder for future planned work.
AUTHOR:
TESTS:
sage: L = J0(37)[0].padic_lseries(5)
sage: loads(dumps(L)) == L
True
sage: L = J0(37)[0].lseries()
sage: loads(dumps(L)) == L
True
Bases: sage.structure.sage_object.SageObject
Base class for -series attached to modular abelian varieties.
Return the abelian variety that this -series is attached to.
EXAMPLES:
sage: J0(11).padic_lseries(7).abelian_variety()
Abelian variety J0(11) of dimension 1
Bases: sage.modular.abvar.lseries.Lseries
A complex -series attached to a modular abelian variety.
EXAMPLES:
sage: A = J0(37)
sage: A.lseries()
Complex L-series attached to Abelian variety J0(37) of dimension 2
Return the rational part of this -function at the central critical value 1.
NOTE: This is not yet implemented.
EXAMPLES:
sage: J0(37).lseries().rational_part()
...
NotImplementedError
Bases: sage.modular.abvar.lseries.Lseries
A -adic -series attached to a modular abelian variety.
Return the -th approximation to this -adic -series as a power series in . Each coefficient is a -adic number whose precision is provably correct.
NOTE: This is not yet implemented.
EXAMPLES:
sage: L = J0(37)[0].padic_lseries(5)
sage: L.power_series()
...
NotImplementedError
sage: L.power_series(3,7)
...
NotImplementedError
Return the prime of this -adic -series.
EXAMPLES:
sage: J0(11).padic_lseries(7).prime()
7