# Journal of the Ramanujan Mathematical Society

Volume 37, Issue 3, September 2022 pp. 207–219.

On the arithmetic of Pad\'e approximants to the exponential function

**Authors**:
John Cullinan and Nick Scheel

**Author institution:**Department of Mathematics, Bard College, Annandale-On-Hudson, NY 12504

**Summary: **
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.

Contents
Full-Text PDF