TY  - BOOK
AU  - Bartolo,Enrique Artal
AU  - Cassou-Noguès,Pierrette
AU  - Luengo,Ignacio
AU  - Hernandez,Melle
TI  - Quasi-Ordinary Power Series and Their Zeta Functions
T2  - Memoirs of the American Mathematical Society
SN  - 9781470404420
AV  - QA614.58 -- .A78 2005eb 
U1  - 510 s;516.3/5 
PY  - 2005///
CY  - Providence
PB  - American Mathematical Society
KW  - Singularities (Mathematics)
KW  - Power series
KW  - Functions, Zeta
KW  - Electronic books
N1  - Intro -- Contents -- Introduction -- Chapter 1. Motivic integration -- 1. Grothendieck ring of varieties -- 2. The arc space of a variety -- 3. Local Denef-Loeser motivic zeta function -- Chapter 2. Generating functions and Newton polyhedra -- 1. Generating functions for integer points in rational polyhedra -- 2. Motivic zeta function and Newton polyhedra -- Chapter 3. Quasi-ordinary power series -- 1. Characteristic exponents -- 2. Newton polyhedron and good coordinates -- 3. Dual decomposition -- 4. Newton map associated with a Newton component -- 5. Transversal sections of a quasi-ordinary power series -- Chapter 4. Denef-Loeser motivic zeta function under the Newton maps -- 1. Vertices of the dual decomposition -- 2. Edges of the Newton polytope -- 3. Zeta functions along strata -- Chapter 5. Consequences of the main theorems -- 1. Essential variables -- 2. Curve case -- 3. The topological zeta function -- 4. A special candidate pole -- Chapter 6. Monodromy conjecture for quasi-ordinary power series -- 1. Monodromy conjecture for curves -- 2. Monodromy conjecture: general case -- 3. Monodromy conjecture for the Igusa zeta-function -- Bibliography
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114116
ER  -