论文标题
Équationde pell-abel et应用
Équation de Pell-Abel et applications
论文作者
论文摘要
在本文中，我们表明，当$ g $ $ g $的一些真正的pell-abel方程$ r $的解决方案时，仅当$ r> g $时。专家已知的结果有后果，专家似乎未知。首先，我们在每$（k，g）\ neq（2,2）$的订单$ g（2g-2）$中，推断出在属$ g $的过度曲线上的原始$ k $ differential。此外，我们表明存在一个非WeierStrass点$ n $ modulo a Weierstrass点，在$ g $ $ g $的过度曲线上，并且仅当$ n> 2g $。
In this paper, we show that there are solutions of every degree $r$ of the equation of Pell-Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$. This result, which is known to the experts, has consequences, which seem to be unknown to the experts. First, we deduce the existence of a primitive $k$-differential on an hyperelliptic curve of genus $g$ with a unique zero of order $k(2g-2)$ for every $(k,g)\neq(2,2)$. Moreover, we show that there exists a non Weierstrass point of order $n$ modulo a Weierstrass point on a hyperelliptic curve of genus $g$ if and only if $n > 2g$.
