Hypertranscendence and linear difference equations, the exponential case
Abstract
In this paper we study meromorphic functions solutions of linear shift difference equations in coefficients in $\mathbb{C}(x)$ involving the operator $\rho: y(x)\mapsto y(x+h)$, for some $h\in \mathbb{C}^*$. We prove that if $f$ is solution of an algebraic differential equation, then $f$ belongs to a ring that is made with periodic functions and exponentials. Our proof is based on the parametrized difference Galois theory initiated by Hardouin and Singer.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.00388
 arXiv:
 arXiv:2212.00388
 Bibcode:
 2022arXiv221200388D
 Keywords:

 Mathematics  Number Theory;
 39A06;
 12H05