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3
votes
0answers
96 views

Discriminant polynomial generalizing the usual discriminant

I wonder if anybody has seen the following natural polynomial. Given a monic univariate polynomial $P(z)$ of degree $N$, denote its roots by $z_1,..., z_N$. Now form a new polynomial $Q(z)$ of ...
2
votes
0answers
62 views

Genus 2 hyperelliptic cryptography : typical discriminant and class number

As far as I know, there is no standard yet for cryptography based on the DLP over Jacobians of genus 2 curves. Yet, what can we say about the class number, and the discriminant of the complex ...
2
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0answers
141 views

Discriminants of Clifford algebras

I have a Clifford algebra defined over a field of characteristic not equal to 2. Is there a formula for its discriminant in terms of the corresponding symmetric bilinear form (or in terms of its ...
1
vote
0answers
100 views

Discriminant of a compositum of number fields, a bound?

Given two number fields $E$ and $F$, is there a bound on $|d_{EF}|$, the absolute value of the absolute discriminant of the compositum of fields $EF$, in terms of $d_E$, $d_F$, and the extension ...