Every divisor [itex]D[/itex] associated to a hyperelliptic curve over [itex]\mathbb{F}_q[/itex] can be represented by a couple of polynomials [itex]D=div(a(x),b(x))[/itex] (Mumfor representation):(adsbygoogle = window.adsbygoogle || []).push({});

http://www.google.it/url?url=http:/...pyTszxEIfDtAa5yaGDBw&ved=0CCMQygQwAA&cad=rja"

A divisor [itex]D[/itex] is prime if [itex]a(x)[/itex] is irreducible over [itex]\mathbb{F}_q[/itex].

I'm trying to prove that a semi-reduced divisor can be written as a combination of prime divisors factoring [itex]a(x) [/itex]:

if [itex]a(x)=\prod a_{i}(x)^{c_i} [/itex], then [itex]D=\sum c_i div(a_i(x),y-b_i(x))[/itex], where [itex]b_i \equiv b \textit{mod}a_i[/itex]

I've some problems with [itex]y-b_i(x)[/itex], any ideas?

(I think the author of the article had some notation problems, if we express [itex]D=div(a(x),b(x))[/itex] it should be [itex]D=\sum c_i div(a_i(x),b_i(x))[/itex], where [itex]D=div(a(x),b(x))[/itex] means [itex]D=gcd (div(a(x)),div(y-b(x)))[/itex] )

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prime divisors hyperelliptic curves

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**