Quasi Ordinary Power Series And Their Zeta Functions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quasi Ordinary Power Series And Their Zeta Functions PDF full book. Access full book title Quasi Ordinary Power Series And Their Zeta Functions.
| Author | : Enrique Artal-Bartolo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 100 |
| Release | : 2005-10-05 |
| Genre | : Functions, Zeta |
| ISBN | : 9780821865637 |
Download Quasi-Ordinary Power Series and Their Zeta Functions Book in PDF, ePub and Kindle
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.
| Author | : José Ignacio Cogolludo-Agustín |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 496 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821848909 |
Download Topology of Algebraic Varieties and Singularities Book in PDF, ePub and Kindle
This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honour of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain.
| Author | : Bart Bories |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 146 |
| Release | : 2016-06-21 |
| Genre | : Mathematics |
| ISBN | : 147041841X |
Download Igusa's $p$-Adic Local Zeta Function and the Monodromy Conjecture for Non-Degenerate Surface Singularities Book in PDF, ePub and Kindle
In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.
| Author | : Antonio Campillo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821869000 |
Download Zeta Functions in Algebra and Geometry Book in PDF, ePub and Kindle
Contains the proceedings of the Second International Workshop on Zeta Functions in Algebra and Geometry held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
| Author | : Gert-Martin Greuel |
| Publisher | : Springer |
| Total Pages | : 604 |
| Release | : 2018-09-18 |
| Genre | : Mathematics |
| ISBN | : 3319968270 |
Download Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics Book in PDF, ePub and Kindle
This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.
| Author | : Christoph Lossen |
| Publisher | : Cambridge University Press |
| Total Pages | : 412 |
| Release | : 2006-04-06 |
| Genre | : Computers |
| ISBN | : 9780521683098 |
Download Singularities and Computer Algebra Book in PDF, ePub and Kindle
A collection of articles giving overviews and open questions in singularities and their computational aspects.
| Author | : Nathanial Patrick Brown |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 122 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821839160 |
Download Invariant Means and Finite Representation Theory of $C^*$-Algebras Book in PDF, ePub and Kindle
Various subsets of the tracial state space of a unital C$*$-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II$ 1$-factor representations of a class of C$*$-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II$ 1$-factor representations. In addition to developing some general theory we also show that these ideas are related to numerous other problems inoperator algebras.
| Author | : William Craig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 298 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821841491 |
Download Semigroups Underlying First-Order Logic Book in PDF, ePub and Kindle
Boolean, relation-induced, and other operations for dealing with first-order definability Uniform relations between sequences Diagonal relations Uniform diagonal relations and some kinds of bisections or bisectable relations Presentation of ${\mathbf S}_q$, ${\mathbf S}_p$ and related structures Presentation of ${\mathbf S}_{pq}$, ${\mathbf S}_{pe}$ and related structures Appendix. Presentation of ${\mathbf S}_{pqe}$ and related structures Bibliography Index of symbols Index of phrases and subjects List of relations involved in presentations Synopsis of presentations
| Author | : Gelu Popescu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821839128 |
Download Entropy and Multivariable Interpolation Book in PDF, ePub and Kindle
We define a new notion of entropy for operators on Fock spaces and positive multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (e.g., multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive multi-Toeplitz kernels on free semigroups (resp. multi-analytic operators) and consequences concerning the extreme points of the unit ball of the noncommutative analytic Toeplitz algebra $F ninfty$. We obtain several geometric characterizations of the central intertwining lifting, a maximal principle, and a permanence principle for the noncommutative commutant lifting theorem. Under certain natural conditions, we find explicit forms for the maximal entropy solution of this multivariable commutant lifting theorem. All these results are used to solve maximal entropy interpolation problems in several variables. We obtain explicit forms for the maximal entropy solution (as well as its entropy) of the Sarason, Caratheodory-Schur, and Nevanlinna-Pick type interpolation problems for the noncommutative (resp. commutative) analytic Toeplitz algebra $F ninfty$ (resp. $W ninfty$) and their tensor products with $B({\mathcal H , {\mathcal K )$. In particular, we provide explicit forms for the maximal entropy solutions of several interpolation problems on the unit ball of $\mathbb{C n$.
| Author | : Takuro Mochizuki |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 262 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821839438 |
Download Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 Book in PDF, ePub and Kindle
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regularholonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
