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Zeta Functions In Algebra And Geometry
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Book Synopsis Zeta Functions in Geometry by : Kurokawa N. (Nobushige)
Download or read book Zeta Functions in Geometry written by Kurokawa N. (Nobushige) and published by . This book was released on 1992 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains accounts of work presented during the research conference, ``Zeta Functions in Geometry,'' held at the Tokyo Institute of Technology in August 1990. The aim of the conference was to provide an opportunity for the discussion of recent results by geometers and number theorists on zeta functions in several different categories. The exchange of ideas produced new insights on various geometric zeta functions, as well as the classical zeta functions. The zeta functions covered here are the Selberg zeta functions, the Ihara zeta functions, spectral zeta functions, and those associated with prehomogeneous vector spaces. Accessible to graduate students with background in geometry and number theory, Zeta Functions in Geometry will prove useful for its presentation of new results and up-to-date surveys.
Book Synopsis Zeta Functions in Algebra and Geometry by : Antonio Campillo
Download or read book Zeta Functions in Algebra and Geometry written by Antonio Campillo and published by American Mathematical Soc.. This book was released on 2012 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume 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. Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. 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. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).
Book Synopsis Zeta-functions by : Alan David Thomas
Download or read book Zeta-functions written by Alan David Thomas and published by Pitman Publishing. This book was released on 1977 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Zeta-functions written by A. D. Thomas and published by . This book was released on 1977 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Zeta Functions in Algebra and Geometry by : Antonio Campillo
Download or read book Zeta Functions in Algebra and Geometry written by Antonio Campillo and published by American Mathematical Soc.. This book was released on 2012-01-01 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Zeta Functions, Topology and Quantum Physics by : Takashi Aoki
Download or read book Zeta Functions, Topology and Quantum Physics written by Takashi Aoki and published by Springer Science & Business Media. This book was released on 2008-05-10 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.
Book Synopsis An Introduction to the Theory of Local Zeta Functions by : Jun-ichi Igusa
Download or read book An Introduction to the Theory of Local Zeta Functions written by Jun-ichi Igusa and published by American Mathematical Soc.. This book was released on 2000 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Book Synopsis Fractal Geometry and Number Theory by : Michel L. Lapidus
Download or read book Fractal Geometry and Number Theory written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.
Book Synopsis Zeta and L-Functions of Varieties and Motives by : Bruno Kahn
Download or read book Zeta and L-Functions of Varieties and Motives written by Bruno Kahn and published by Cambridge University Press. This book was released on 2020-05-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Book Synopsis Zeta and L-Functions of Varieties and Motives by : Bruno Kahn
Download or read book Zeta and L-Functions of Varieties and Motives written by Bruno Kahn and published by Cambridge University Press. This book was released on 2020-05-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how zeta and L-functions have shaped the development of major parts of mathematics over the past two centuries.
Book Synopsis Dynamical, Spectral, and Arithmetic Zeta Functions by : Michel Laurent Lapidus
Download or read book Dynamical, Spectral, and Arithmetic Zeta Functions written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2001 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.
Book Synopsis Quasi-Ordinary Power Series and Their Zeta Functions by : Enrique Artal-Bartolo
Download or read book Quasi-Ordinary Power Series and Their Zeta Functions written by Enrique Artal-Bartolo and published by American Mathematical Soc.. This book was released on 2005-10-05 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves by : Spencer J. Bloch
Download or read book Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves written by Spencer J. Bloch and published by American Mathematical Soc.. This book was released on 2000 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief hardcover is a classic title covering a renowned series of lectures. A mathematical jewel.
Book Synopsis Fractal Geometry, Complex Dimensions and Zeta Functions by : Michel L. Lapidus
Download or read book Fractal Geometry, Complex Dimensions and Zeta Functions written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
Book Synopsis Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion by : Alexander Fel'shtyn
Download or read book Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion written by Alexander Fel'shtyn and published by American Mathematical Soc.. This book was released on 2000 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Book Synopsis Zeta Functions of Groups and Rings by : Marcus du Sautoy
Download or read book Zeta Functions of Groups and Rings written by Marcus du Sautoy and published by Springer Science & Business Media. This book was released on 2008 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.
Book Synopsis Exploring the Riemann Zeta Function by : Hugh Montgomery
Download or read book Exploring the Riemann Zeta Function written by Hugh Montgomery and published by Springer. This book was released on 2017-09-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
