< Back to previous page

Publication

Zeta functions and oscillatory integrals for meromorphic functions

Journal Contribution - Journal Article

© 2017 Elsevier Inc. In the 70's Igusa developed a uniform theory for local zeta functions and oscillatory integrals attached to polynomials with coefficients in a local field of characteristic zero. In the present article this theory is extended to the case of rational functions, or, more generally, meromorphic functions f/g, with coefficients in a local field of characteristic zero. This generalization is far from being straightforward due to the fact that several new geometric phenomena appear. Also, the oscillatory integrals have two different asymptotic expansions: the ‘usual’ one when the norm of the parameter tends to infinity, and another one when the norm of the parameter tends to zero. The first asymptotic expansion is controlled by the poles (with negative real parts) of all the twisted local zeta functions associated to the meromorphic functions f/g−c, for certain special values c. The second expansion is controlled by the poles (with positive real parts) of all the twisted local zeta functions associated to f/g.
Journal: Advances in Mathematics
ISSN: 0001-8708
Volume: 311
Pages: 295 - 337
Publication year:2017
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:3
CSS-citation score:2
Authors:International
Authors from:Higher Education