Take for example, the function:(adsbygoogle = window.adsbygoogle || []).push({});

[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

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

Can you offer guidance or do you also need help?

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