# Hyperexponential solutions of elliptic difference equations

@inproceedings{Combot2022HyperexponentialSO, title={Hyperexponential solutions of elliptic difference equations}, author={Thierry Combot}, year={2022} }

Consider an elliptic curve C with coeﬃcients in K with [ K : Q ] < ∞ and δ ∈ C ( K ) a non torsion point. We consider an elliptic diﬀerence equation P li =0 a i ( p ) f ( p ⊕ i.δ ) = 0 with ⊕ the elliptic addition law and a i polynomials on 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 ⊕ δ ) /f ( p ) is rational over C .

## One Citation

### Computation of the difference Galois groups of order three equations

- Mathematics
- 2022

. In this paper we explain how to compute the diﬀerence Galois groups of order three equations for a large class of diﬀerence operators including the shift operator (Case S), the q -diﬀerence…

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