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On a Conjecture of Igusa in Two Dimensions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 142, Number 4, August 2020
- pp. 1193-1238
- 10.1353/ajm.2020.0026
- Article
- Additional Information
abstract:
We extend work of Denef and Sperber and also Cluckers regarding a conjecture of Igusa in the two dimensional setting by no longer requiring the polynomial to be nondegenerate with respect to its Newton diagram. More precisely we establish sharp, uniform bounds for complete exponential sums and the number of polynomial congruences for general quasi-homogeneous polynomials in two variables.