Uniform bounds for derivatives of definable functions with a diophantine application
Presenter
May 14, 2014
Keywords:
- complex analysis
- uniform estimate
- uniform family
- definable functions
- definable families of holomorphic maps
- model theory
- analytic continuation
- Diophantine geometry
MSC:
- 11J91
- 11J97
- 11Jxx
- 11-xx
- 03Cxx
- 03C64
Abstract
I discuss the problem of determining those (unary) functions definable in R_{an, exp} that take integer values for positive integer arguments, improving upon a result of Jones and Thomas. The key new technique involves extending such functions to sectors in the complex plane without increasing their rate of growth by too much.