论文标题
椭圆曲线线性系统中的线性独立性
Linear independence in linear systems on elliptic curves
论文作者
论文摘要
让$ e $为椭圆曲线，带有身份$ o $，让$ c $是奇数订单$ n $的环状亚组，在代数封闭的字段$ k $带有$ \ operatatorName {char} k \ nmid n $上。对于$ p \在c $中，让$ s_p $是Divisor $ n \ cdot p -n \ cdot o $的合理函数。我们询问$ n $函数$ s_p $是否线性独立。对于通用$（e，c）$，我们证明答案是肯定的。当$ n $是$ x_1（n）$的几何形状时，我们限制了特殊$（e，c）$的数量。问题可以是根据$ e $的任意程度$ n $ line Bundle的各个部分进行重铸。
Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic subgroup of odd order $N$, over an algebraically closed field $k$ with $\operatorname{char} k \nmid N$. For $P \in C$, let $s_P$ be a rational function with divisor $N \cdot P - N \cdot O$. We ask whether the $N$ functions $s_P$ are linearly independent. For generic $(E,C)$, we prove that the answer is yes. We bound the number of exceptional $(E,C)$ when $N$ is a prime by using the geometry of the universal generalized elliptic curve over $X_1(N)$. The problem can be recast in terms of sections of an arbitrary degree $N$ line bundle on $E$.
