### Navigation

- index
- modules |
- previous |
- Modular Abelian Varieties »

# \(L\)-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

### Navigation

- index
- modules |
- previous |
- Modular Abelian Varieties »