Michel Waldschmidt's Books

Diophantine Approximation on Linear Algebraic Groups

Transcendence Properties of the Exponential Function in Several Variables

By: Michel Waldschmidt

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Diophantine Approximation on Linear Algebraic Groups

Transcendence Properties of the Exponential Function in Several Variables

By: Michel Waldschmidt

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

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649

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Springer Science & Business Media

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ISBN 10

3662115697

ISBN 13

9783662115695

Diophantine Approximation

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000

By: David Masser,Yuri V. Nesterenko,Hans Peter Schlickewei,Wolfgang M. Schmidt,Michel Waldschmidt

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Diophantine Approximation

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000

By: David Masser,Yuri V. Nesterenko,Hans Peter Schlickewei,Wolfgang M. Schmidt,Michel Waldschmidt

Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.

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359

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Springer

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ISBN 10

3540449795

ISBN 13

9783540449799

Number Theory

Ramanujan Mathematical Society, January 3-6, 1996, Tiruchirapalli, India

By: Michel Waldschmidt

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Number Theory

Ramanujan Mathematical Society, January 3-6, 1996, Tiruchirapalli, India

By: Michel Waldschmidt

To observe the tenth anniversary of the founding of the Ramanujan Mathematical Society, an international conference on Discrete Mathematics and Number Theory was held in January 1996 in Tiruchirapalli, India. This volume contains proceedings from the number theory component of that conference. Papers are divided into four groups: arithmetic algebraic geometry, automorphic forms, elementary and analytic number theory, and transcendental number theory. This work deals with recent progress in current aspects of number theory and covers a wide variety of topics.

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410

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806068

ISBN 13

9780821806067

Handbook of Floating-Point Arithmetic

By: Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres

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Handbook of Floating-Point Arithmetic

By: Jean-Michel Muller,Nicolas Brisebarre,Florent de Dinechin,Claude-Pierre Jeannerod,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Damien Stehlé,Serge Torres

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

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579

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817647058

ISBN 13

9780817647056

Noise, Oscillators and Algebraic Randomness

From Noise in Communication Systems to Number Theory

By: Michel Planat

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Noise, Oscillators and Algebraic Randomness

From Noise in Communication Systems to Number Theory

By: Michel Planat

Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a school in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999, by engineers, physisicts and mathematicians.

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417

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Springer

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ISBN 10

3540454632

ISBN 13

9783540454632

The LaTex Graphics Companion

Illustrating Documents with TeX and PostScript

By: Michel Goossens,S. P. Q. Rahtz,Frank Mittelbach

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The LaTex Graphics Companion

Illustrating Documents with TeX and PostScript

By: Michel Goossens,S. P. Q. Rahtz,Frank Mittelbach

Complementing The LaTeX Companion, this new graphics companion addresses one of the most common needs among users of the LaTeX typesetting system: the incorporation of graphics into text. It provides the first full description of the standard LaTeX color and graphics packages, and shows how you can combine TeX and PostScript capabilities to produce beautifully illustrated pages. You will learn how to incorporate graphic files into a LaTeX document, program technical diagrams using several different languages, and achieve special effects with fragments of embedded PostScript. Furthermore, you'll find detailed descriptions of important packages like Xy-pic, PSTricks, and METAPOST; the dvips dvi to PostScript driver; and Ghostscript.

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620

Publisher

Addison-Wesley Professional

Published Date

ISBN 10

0201854694

ISBN 13

9780201854695

The Feynman Integral and Feynman's Operational Calculus

By: Gerald W. Johnson,Michel L. Lapidus

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The Feynman Integral and Feynman's Operational Calculus

By: Gerald W. Johnson,Michel L. Lapidus

This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.

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790

Publisher

Clarendon Press

Published Date

ISBN 10

0191546267

ISBN 13

9780191546266

In Search of the Riemann Zeros

Strings, Fractal Membranes and Noncommutative Spacetimes

By: Michel Laurent Lapidus

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In Search of the Riemann Zeros

Strings, Fractal Membranes and Noncommutative Spacetimes

By: Michel Laurent Lapidus

Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possible--or, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line.

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594

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842226

ISBN 13

9780821842225

Geometry of Cuts and Metrics

By: Michel Marie Deza,Monique Laurent

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Geometry of Cuts and Metrics

By: Michel Marie Deza,Monique Laurent

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.

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580

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Springer

Published Date

ISBN 10

3642042953

ISBN 13

9783642042959

Analysis and Geometry of Markov Diffusion Operators

By: Dominique Bakry,Ivan Gentil,Michel Ledoux

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Analysis and Geometry of Markov Diffusion Operators

By: Dominique Bakry,Ivan Gentil,Michel Ledoux

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.

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555

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Springer Science & Business Media

Published Date

ISBN 10

3319002279

ISBN 13

9783319002279

Elementary Functions:

Algorithms and Implementation

By: Jean-Michel Muller

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Elementary Functions:

Algorithms and Implementation

By: Jean-Michel Muller

Second Edition of successful, well-reviewed Birkhauser book, which sold 866 copies in North America Provides an up-to-date presentation by including new results, examples, and problems throughout the text The second edition adds a chapter on multiple-precision arithmetic, and new algorithms invented since 1997

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211

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Springer Science & Business Media

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ISBN 10

1475726465

ISBN 13

9781475726466

Fractal Zeta Functions and Fractal Drums

Higher-Dimensional Theory of Complex Dimensions

By: Michel L. Lapidus,Goran Radunović,Darko Žubrinić

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Fractal Zeta Functions and Fractal Drums

Higher-Dimensional Theory of Complex Dimensions

By: Michel L. Lapidus,Goran Radunović,Darko Žubrinić

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.

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685

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Springer

Published Date

ISBN 10

3319447068

ISBN 13

9783319447063

Dynamical, Spectral, and Arithmetic Zeta Functions

AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas

By: Michel Laurent Lapidus,Machiel Van Frankenhuysen

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Dynamical, Spectral, and Arithmetic Zeta Functions

AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 15-16, 1999, San Antonio, Texas

By: Michel Laurent Lapidus,Machiel Van Frankenhuysen

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.

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210

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820796

ISBN 13

9780821820797

Introduction to Complex Reflection Groups and Their Braid Groups

By: Michel Broué

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Introduction to Complex Reflection Groups and Their Braid Groups

By: Michel Broué

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.

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150

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Springer

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ISBN 10

3642111750

ISBN 13

9783642111754

Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

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Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

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374

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Springer

Published Date

ISBN 10

3642146600

ISBN 13

9783642146602

Optimal Transportation Networks

Models and Theory

By: Marc Bernot,Vicent Caselles,Jean-Michel Morel

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Optimal Transportation Networks

Models and Theory

By: Marc Bernot,Vicent Caselles,Jean-Michel Morel

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

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204

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Springer Science & Business Media

Published Date

ISBN 10

3540693149

ISBN 13

9783540693147

Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

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Mixed Finite Elements, Compatibility Conditions, and Applications

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006

By: Daniele Boffi,Franco Brezzi,Leszek F. Demkowicz,Ricardo G. Durán,Richard S. Falk,Michel Fortin

Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

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