论文标题
关于指数函数的Padé近似值的算术
On the arithmetic of Padé approximants to the exponential function
论文作者
论文摘要
$（u，v）$ - padé近似与函数$ f $的近似是（唯一的，延展）有理近似$ f（x）= p（x）/q（x）/q（x）+o（x^{x^{u+v+1}）$，其中$ p $ a $ $ $ u $ and $ u $ and $ q $ a $ $ v $ v $。由Molin，Pazuki和Rabarison的最新工作激励，我们研究了指数多项式的Padé近似值的算术。通过将近似值视为某些广义的laguerre多项式，我们确定了对角近似值的Galois基团，并证明了一些特殊的不可约性案例。
The $(u,v)$-Padé approximation to a function $f$ is the (unique, up to scaling) rational approximation $f(x) = P(x)/Q(x) + O(x^{u+v+1})$, where $P$ has degree $u$ and $Q$ has degree $v$. Motivated by recent work of Molin, Pazuki, and Rabarison, we study the arithmetic of the Padé approximants of the exponential polynomials. By viewing the approximants as certain Generalized Laguerre Polynomials, we determine the Galois groups of the diagonal approximants and prove some special cases of irreducibility.
