5 citations · 8 across the 9 of their papers we have counts for
11 papers
The Igusa local zeta function of certain Thom-Sebastiani type functions
Quy Thuong Lê, Hoang Long Nguyen
In this paper, we give an explicit formula of the Igusa local zeta function of a Thom-Sebastiani type sum of two separated-variable Newton non-critical polynomials. Data for the de…
The -adic zeta function of a plane curve singularity
Huyen Trang Hoang, Quy Thuong Lê, Hoang Long Nguyen
Using toric modifications and some compatibility we compute the local -adic zeta function of a plane curve singularity. Thanks to the compatibility, we can work over the analyti…
Higher Jacobian ideals, contact equivalence and motivic zeta functions
Quy Thuong Lê, Takehiko Yasuda
We show basic properties of higher Jacobian matrices and higher Jacobian ideals for functions and apply it to obtain two results concerning singularities of functions. Firstly, we…
Equivariant motivic integration on special formal schemes
Quy Thuong Lê, Hong Duc Nguyen
In this article, we construct an equivariant version of motivic integration on special formal schemes that generalizes our previous work for algebraic varieties. Pointing out the e…
Grothendieck rings of definable subassignments and equivariant motivic measures
Quy Thuong Le
The paper studies categories of definable subassignments with some category equivalences to semi-algebraic and constructible subsets of arc spaces of algebraic varieties. These mat…
Topological zeta functions of complex plane curve singularities
Quy Thuong Lê, Khanh Hung Nguyen
We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that t…
Cohomology of contact loci
Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê +1
We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in term…
Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci
Quy Thuong Lê, Tat Thang Nguyen
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on conta…
Equivariant motivic integration and proof of the integral identity conjecture for regular functions
Quy Thuong Lê, Hong Duc Nguyen
We develop the Denef-Loeser motivic integration to the equivariant motivic integration and use it to prove the full integral identity conjecture for regular functions.
Euler reflexion formulas for motivic multiple zeta functions
Quy Thuong Le, Hong Duc Nguyen
We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and co…
A proof of the integral identity conjecture, II
Lê Quy Thuong
In this note, using Cluckers-Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arb…