论文标题
关于计算差异三个方程式的差异galois组
On the computation of the difference Galois groups of order three equations
论文作者
论文摘要
在本文中，我们考虑了计算大量差异操作员的订单三个方程式的差异组的问题，包括偏移操作员（案例S），$ q $ - 差异操作员（案例Q），Mahler操作员（案例M）和椭圆情况（case e）。我们表明，总体问题可以简化为几个辅助问题。我们证明了可检测不可约和不可分割的Galois群体的标准。最后，我们给出了订单三个差异方程解决方案解决方案解决方案解决方案的足够条件。我们还计算了Wadim Zudilin建议的方程式的差异GALOIS组。
In this paper we consider the problem of computing the difference Galois groups of order three equations for a large class of difference operators including the shift operator (Case S), the $q$-difference operator (Case Q), the Mahler operator (Case M) and the elliptic case (Case E). We show that the general problem can be reduced to several ancillary problems. We prove criteria to detect the irreducible and imprimitive Galois groups. Finally, we give a sufficient condition of differential transcendence of solutions of order three difference equations. We also compute the difference Galois group of an equation suggested by Wadim Zudilin.
