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How many distinct ways can an algebraic function fully-ramify?

  1. Oct 17, 2012 #1
    Take for example, the function:

    [tex]a_0(z)+a_1(z)w+a_2(z)w^2+a_3(z) w^3+a_4(z)w^4+a_5(z)w^5=0[/tex]

    with the degree of [itex] a_n(z)[/itex] also five.

    What are necessary or sufficient conditions imposed on the polynomials [itex]a_n(z)[/itex] to cause [itex]w(z)[/itex] to fully-ramify at the origin?

    I can easily think of one sufficient condition:

    [tex]z-w^5=0[/tex]

    Can we do better than that?

    Also, can anyone give me a reference where this type of problem may be addressed? I do have several texts on algebraic functions but can't find anything about it.

    Thanks,
    Jack
     
    Last edited: Oct 17, 2012
  2. jcsd
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