\(L\)-series of modular abelian varieties¶
At the moment very little functionality is implemented – this is mostly a placeholder for future planned work.
AUTHOR:
- William Stein (2007-03)
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
-
class
sage.modular.abvar.lseries.
Lseries
(abvar)¶ Bases:
sage.structure.sage_object.SageObject
Base class for \(L\)-series attached to modular abelian varieties.
-
abelian_variety
()¶ Return the abelian variety that this \(L\)-series is attached to.
- OUTPUT:
- a modular abelian variety
EXAMPLES:
sage: J0(11).padic_lseries(7).abelian_variety() Abelian variety J0(11) of dimension 1
-
-
class
sage.modular.abvar.lseries.
Lseries_complex
(abvar)¶ Bases:
sage.modular.abvar.lseries.Lseries
A complex \(L\)-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
-
rational_part
()¶ Return the rational part of this \(L\)-function at the central critical value 1.
NOTE: This is not yet implemented.
EXAMPLES:
sage: J0(37).lseries().rational_part() Traceback (most recent call last): ... NotImplementedError
-
-
class
sage.modular.abvar.lseries.
Lseries_padic
(abvar, p)¶ Bases:
sage.modular.abvar.lseries.Lseries
A \(p\)-adic \(L\)-series attached to a modular abelian variety.
-
power_series
(n=2, prec=5)¶ Return the \(n\)-th approximation to this \(p\)-adic \(L\)-series as a power series in \(T\). Each coefficient is a \(p\)-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() Traceback (most recent call last): ... NotImplementedError sage: L.power_series(3,7) Traceback (most recent call last): ... NotImplementedError
-
prime
()¶ Return the prime \(p\) of this \(p\)-adic \(L\)-series.
EXAMPLES:
sage: J0(11).padic_lseries(7).prime() 7
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