Quasi-Ordinary Power Series and Their Zeta Functions.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.