On the Igusa conjecture in two dimensions

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1193-1238
JournalAmerican Journal of Mathematics
Issue number4
Publication statusPublished - 31 Aug 2020


  • math.CA
  • 11A07, 11L07, 11L40, 42B20


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