• Corpus ID: 248496640

Hyperexponential solutions of elliptic difference equations

  title={Hyperexponential solutions of elliptic difference equations},
  author={Thierry Combot},
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 . 
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The arithmetic of elliptic curves, volume 106

  • 2009