In Lemma 8 of the paper "Constant terms in powers of a Laurent polynomial" (by J.J. Duistermaat and Wilberd van der Kallen) the exponent $\alpha$ in the asymptotic expansion of a function of Nilsson class near a singular point is shown to satisfy $\alpha > -1$ and I am looking for references (not already mentioned in this paper) which prove such an estimate by any means. I really need such an estimate in my own work and so I am interested in any method that accomplishes this.
It is so important to me that I am learning algebraic geometry especially for this even though I am more an analyst. I have pretty much sacrificed everything for the past 5 years for this research and now it all comes down to this. Any help would be infinitely appreciated. Thank you.
Please see also this question, aimed at trying to understand the proof of Lemma 8 of the above mentioned paper, which I have just updated and might be easier to answer now.
UPDATE:
'Singularities of Differentiable Maps', Volume 2, by Arnold et al., has some results on this.
'Singularities of integrals' by Pham, has some relevant background information.
