Acknowledgements ................................................ 3
1. Introduction ................................................. 5
2. A Brief Outline of Nevanlinna Theory ......................... 6
3. Difference Equations and Meromorphic Solutions ............... 8
3.1. Equations with constant coefficients .................... 8
3.2. Earlier results involving Nevanlinna theory ............. 9
3.3. The main results ....................................... 11
3.4. Nevanlinna theory and difference equations ............. 17
4. The Family of Difference Painlevé III ....................... 22
4.1. Preliminaries .......................................... 22
4.2. Equations with q = 2 ................................... 23
4.3. Equations with q = 0 ................................... 32
4.4. Equations with q - 1 ................................... 32
5. The Family of Difference Painlevé V ......................... 38
5.1. Preliminaries .......................................... 38
5.2. Points where Q vanishes ................................ 40
5.3. Points where ww — 1 vanishes ........................... 44
5.4. Restriction of the coefficients ........................ 48
6. Discussion .................................................. 51
6.1. Summary and review of the results ...................... 51
6.2. Open questions ......................................... 54
6.3. Alternative approaches ................................. 54
References ..................................................... 57
| 
