论文标题
椭圆差方程的过度解决方案
Hyperexponential solutions of elliptic difference equations
论文作者
论文摘要
考虑一个椭圆曲线$ \ MATHCAL {C} $，带有$ \ Mathbb {K} $的系数，带有$ [\ Mathbb {k {k}：\ Mathbb {q}] <\ infty $和$ unfty $和$δ\ in \ Mathcal {C}（c}（c}（c}））我们考虑一个椭圆差方程$ \ sum_ {i = 0}^l a_i（p）f（p \ oplusi.δ）= 0 $ with $ \ oplus $ eelliptic添加法和$ a_i $ polynomials on $ \ nathcal {c} $。我们提出了一种计算有理解决方案的算法，然后是一个中介类，我们称为伪理性解决方案，最后是HypereXponential Solutions，该解决方案是函数$ f $，因此$ f（p \oplusΔ）/f（p）$是$ \ nathcal {c} $的合理的。
Consider an elliptic curve $\mathcal{C}$ with coefficients in $\mathbb{K}$ with $[\mathbb{K}:\mathbb{Q}]<\infty$ and $δ\in \mathcal{C}(\mathbb{K})$ a non torsion point. We consider an elliptic difference equation $\sum_{i=0}^l a_i(p) f(p\oplus i.δ)=0$ with $\oplus$ the elliptic addition law and $a_i$ polynomials on $\mathcal{C}$. We present an algorithm to compute rational solutions, then an intermediary class we call pseudo-rational solutions, and finally hyperexponential solutions, which are functions $f$ such that $f(p\oplus δ)/f(p)$ is rational over $\mathcal{C}$.
