Exponential sums: questions by Denef, Sperber, and Igusa
| dc.creator | Cluckers, R. | |
| dc.date | 2007-11-21 | |
| dc.date.accessioned | 2026-07-07T08:44:14Z | |
| dc.date.available | 2026-07-07T08:44:14Z | |
| dc.description | We prove the remaining part of the conjecture by Denef and Sperber [Denef, J. and Sperber, S., \textit{Exponential sums mod $p^n$ and {N}ewton polyhedra}, Bull. Belg. Math. Soc., {\bf{suppl.}} (2001) 55-63] on nondegenerate local exponential sums modulo $p^m$. We generalize Igusa's conjecture of the introduction of [Igusa, J., \textit{Lectures on forms of higher degree}, Lect. math. phys., Springer-Verlag, {\bf{59}} (1978)] from the homogeneous to the quasi-homogeneous case and prove the nondegenerate case as well as the modulo $p$ case. We generalize some results by Katz of [Katz, N. M., \textit{Estimates for "singular" exponential sums}, Internat. Math. Res. Notices (1999) no. 16, 875-899] on finite field exponential sums to the quasi-homogeneous case. | |
| dc.identifier | https://arxiv.org/abs/0711.3365 | |
| dc.identifier | http://arxiv.org/abs/0711.3365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142588 | |
| dc.subject | Number Theory | |
| dc.subject | 11L07, 11S40; 11L05 | |
| dc.title | Exponential sums: questions by Denef, Sperber, and Igusa | |
| dc.type | text |