325 citations · 459 across the 11 of their papers we have counts for
4 papers · 1 filter
Nevanlinna theory for the difference operator
R. G. Halburd, R. J. Korhonen
Certain estimates involving the derivative of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose o…
Diophantine Integrability
R. G. Halburd
The heights of iterates of the discrete Painleve equations over number fields appear to grow no faster than polynomials while the heights of generic solutions of non-integrable dis…
Finite-order meromorphic solutions and the discrete Painleve equations
R. G. Halburd, R. J. Korhonen
Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z.…
Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations
R. G. Halburd, R. J. Korhonen
The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a…