Download or read book On Artin s Conjecture for Odd 2 dimensional Representations written by Gerhard Frey and published by Springer. This book was released on 2006-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. To do this, one has to determine the number of all representations with given Artin conductor and determinant and to compute the dimension of a corresponding space of cusp forms of weight 1 which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols. It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.
Download or read book On Artin s Conjecture for Odd 2 Dimensional Representations written by Gerhard Frey and published by . This book was released on 2014-01-15 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Modules and Complete Intersections written by Satya Mandal and published by Springer Science & Business Media. This book was released on 1997-10-10 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions". These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.
Download or read book Moduli of Supersingular Abelian Varieties written by Ke-Zheng Li and published by Springer Science & Business Media. This book was released on 1998-01-19 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Ãg.g/4Ã, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).
Download or read book An Introduction to Analysis on Wiener Space written by Ali S. Üstünel and published by Springer. This book was released on 2006-11-14 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives the basis of the probabilistic functional analysis on Wiener space, developed during the last decade. The subject has progressed considerably in recent years thr- ough its links with QFT and the impact of Stochastic Calcu- lus of Variations of P. Malliavin. Although the latter deals essentially with the regularity of the laws of random varia- bles defined on the Wiener space, the book focuses on quite different subjects, i.e. independence, Ramer's theorem, etc. First year graduate level in functional analysis and theory of stochastic processes is required (stochastic integration with respect to Brownian motion, Ito formula etc). It can be taught as a 1-semester course as it is, or in 2 semesters adding preliminaries from the theory of stochastic processes It is a user-friendly introduction to Malliavin calculus!
Download or read book The Blocking Technique Weighted Mean Operators and Hardy s Inequality written by Karl-Goswin Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 1998-01-19 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first comprehensive treatment of the blocking technique which consists in transforming norms in section form into norms in block form, and vice versa. Such norms appear throughout analysis. The blocking technique is a powerful, yet elementary, tool whose usefulnes is demonstrated in the book. In particular, it is shown to lead to the solution of three recent problems of Bennett concerning the inequalities of Hardy and Copson. The book is addressed to researchers and graduate students. An interesting feature is that it contains a dictionary of transformations between section and block norms and will thus be useful to researchers as a reference text. The book requires no knowledge beyond an introductory course in functional analysis.
Download or read book Flows on 2 dimensional Manifolds written by Igor Nikolaev and published by Springer Science & Business Media. This book was released on 1999-07-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Download or read book S minaire de Probabilit s XXXII written by Jacques Azema and published by Springer. This book was released on 2007-01-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the papers in the volume are original research papers, discussing fundamental properties of stochastic processes. The topics under study (martingales, filtrations, path properties, etc.) represent an important part of the current research performed in 1996-97 by various groups of probabilists in France and abroad.
Download or read book Loeb Measures in Practice Recent Advances written by Nigel J. Cutland and published by Springer. This book was released on 2004-10-11 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.
Download or read book Seminaire de Probabilites XXIX written by Jacques Azema and published by Springer. This book was released on 2006-11-14 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the papers included in this volume are original research papers. They represent an important part of the work of French probabilists and colleagues with whom they are in close contact throughout the world. The main topics of the papers are martingale and Markov processes studies.
Download or read book Introduction To Non abelian Class Field Theory An Automorphic Forms Of Weight 1 And 2 dimensional Galois Representations written by Toyokazu Hiramatsu and published by World Scientific. This book was released on 2016-09-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-06-20 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Download or read book Galois Theory and Modular Forms written by Ki-ichiro Hashimoto and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.
Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Download or read book Integral Geometry Radon Transforms and Complex Analysis written by Carlos A. Berenstein and published by Springer Science & Business Media. This book was released on 1998-04-16 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
Download or read book Polynomial Mappings written by Wladyslaw Narkiewicz and published by Springer. This book was released on 2006-11-14 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
Download or read book Mathematics Unlimited 2001 and Beyond written by Björn Engquist and published by Springer. This book was released on 2017-04-05 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
