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Let $K$ be a number field of absolute degree $d$, let $B$ be a positive real number, and write $S(K, B) = \{x \in K : H(x) \leq B\}$. Here $H$ is the absolute multiplicative height of an algebraic ...

I hope this is a good question. Recently I worked with genus two curves $H$ that have multiplication by $[\zeta_5]\in \text{Aut}(H)$, that is, multiplication by $e^{2\pi i/5}$. This automorphism is ...

Let $r\geq 5$ be a prime. Suppose I have a specified hyperelliptic curve $C: y^2=f(x)$ defined over $\mathbb{Q}$, where $f\in\mathbb{Q}[x]$ has degree $r$. Note: the roots of $f$ are not rational but ...

I implemented the algorithm that Felipe Voloch's suggested in his reply to the question: Subfields of a function field the algorithm is here: Subfields of a function field I considered the ...

I'm asking this question as a follow up to the Felipe Voloch's answer to this question: Subfields of a function field which you can read it here: Subfields of a function field (I just didn't have ...

I read following paragraph from: G. Tamme, Teilkörper höheren Geschlechts eines algebraischen Funktionenkörpers, Arch. Math. 23 (1972), 257--259 Here $C$ is a curve of genus $\ge 2$ and $J$ is the ...