2003
DOI: 10.5802/aif.2001
|View full text |Cite
|
Sign up to set email alerts
|

Motivic-type invariants of blow-analytic equivalence

Abstract: To a given analytic function germ f : (R d , 0) → (R, 0), we associate zeta functions Z f,+ , Z f,− ∈ Z[[T ]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

1
62
0

Year Published

2005
2005
2018
2018

Publication Types

Select...
7

Relationship

1
6

Authors

Journals

citations
Cited by 26 publications
(63 citation statements)
references
References 31 publications
(71 reference statements)
1
62
0
Order By: Relevance
“…In the latter case, additionally, f (x, y) = x p − y q and g(x, y) = x p + y q are blow analytically equivalent, cf. [18], but they are not analytically equivalent. Moreover, f and g are not bi-lipschitz equivalent.…”
Section: Cascade Blow-analytic Homeomorphisms and Their Geometric Promentioning
confidence: 99%
See 3 more Smart Citations
“…In the latter case, additionally, f (x, y) = x p − y q and g(x, y) = x p + y q are blow analytically equivalent, cf. [18], but they are not analytically equivalent. Moreover, f and g are not bi-lipschitz equivalent.…”
Section: Cascade Blow-analytic Homeomorphisms and Their Geometric Promentioning
confidence: 99%
“…We complete the general case in Corollary 2.5 below. Apart from the Fukui invariants, motivic type invariants are introduced in [18] and [5].…”
Section: Invariants Of Blow-analytic Equivalencementioning
confidence: 99%
See 2 more Smart Citations
“…The latter has already been studied with slightly different definitions (see in particular S. Koike & A. Parusiński [11] and T. Fukui & L. Paunescu [7]). Roughly speaking, two given real analytic function germs are blow-analytic equivalent if they are topologicaly equivalent and moreover, after suitable modifications, they become analytically equivalent.…”
mentioning
confidence: 99%