On Archimedean zeta functions and Newton polyhedra
| Autor: | Fuensanta Aroca, Mirna Gómez-Morales, Edwin León-Cardenal |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial
Pure mathematics Applied Mathematics 010102 general mathematics Resolution of singularities Function (mathematics) 01 natural sciences Functional Analysis (math.FA) Orthant Mathematics - Functional Analysis 010101 applied mathematics Mathematics - Algebraic Geometry Polyhedron Hyperplane 42B20 14M25 58K05 14B05 FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Complex number Analysis Local zeta-function Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 473:1215-1233 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2019.01.017 |
| Popis: | Let $f$ be a polynomial function over the complex numbers and let $\phi$ be a smooth function over $\mathbb{C}$ with compact support. When $f$ is non-degenerate with respect to its Newton polyhedron, we give an explicit list of candidate poles for the complex local zeta function attached to $f$ and $\phi$. The provided list is given just in terms of the normal vectors to the supporting hyperplanes of the Newton polyhedron attached to $f$. More precisely, our list does not contain the candidate poles coming from the additional vectors required in the regular conical subdivision of the first orthant, and necessary in the study of local zeta functions through resolution of singularities. Our results refine the corresponding results of Varchenko and generalize the results of Denef and Sargos in the real case, to the complex setting. Comment: 19 pages. Comments welcome! |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect