Download or read book On Invariants and the Theory of Numbers written by Leonard Eugene Dickson and published by Courier Corporation. This book was released on 2004-01-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of enormous historical importance, this classic offered the first public formulation of Dickson's theory of invariants for modular forms and linear transformations. In many sections of the five lectures included here, Dickson aimed not at complete generality, but at an illumination of typical and suggestive topics. The introductory lecture is followed by sections on seminvariants of algebraic and modular binary forms; invariants of a modular group and formal invariants and covariants of modular forms; modular geometry and covariantive theory of a quadratic form in m variables, modulo 2; and a theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry. 1914 ed.

Download or read book On Invariants and the Theory of Numbers written by Leonard Eugene Dickson and published by . This book was released on 1966 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Invariant Theory written by Nolan R. Wallach and published by Springer. This book was released on 2017-09-08 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.

Download or read book On Invariants and the Theory of Numbers written by and published by . This book was released on 1914 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Percy Alexander MacMahon Number theory invariants and applications written by Percy Alexander MacMahon and published by . This book was released on 1978 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by Cambridge University Press. This book was released on 2003-08-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Download or read book On Invariants and the Theory of Numbers written by L. E. Dickson and published by . This book was released on 1915 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Madison Colloquium 1913 written by American Mathematical Society. Colloquium and published by . This book was released on 1914 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book L2 Invariants Theory and Applications to Geometry and K Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Download or read book ON INVARIANTS AND THE THEORY OF NUMBERS written by and published by . This book was released on 1966 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theory of Algebraic Invariants written by David Hilbert and published by Cambridge University Press. This book was released on 1993-11-26 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.

Download or read book On Invariants and the Theory of Numbers written by Leonard Eugene Dickson and published by . This book was released on 1914 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Theory of Generalized Donaldson Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

Download or read book The Madison Colloquium 1913 written by American Mathematical Society. Colloquium and published by . This book was released on 1914 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the tradition of the American Mathematical Society, the seventh colloquium of the Society was held as part of the summer meeting that took place at the University of Wisconsin, in Madison. Two sets of lectures were presented: On Invariants and the Theory of Numbers, by L.E. Dickson, and Functions of Several Complex Variables, by W.F. Osgood. Dickson considers invariants of quadratic forms, with a special emphasis on invariants of forms defined in characteristic p, also called modular invariants, which have number-theoretic consequences. He is able to find a fundamental set of invar.

Download or read book Surveys in Number Theory written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).

Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text

Download or read book History of the Theory of Numbers written by Leonard Eugene Dickson and published by University of Pennsylvania Press. This book was released on 1999 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dickson's History is truly a monumental account of the development of one of the oldest and most important areas of mathematics. It is remarkable today to think that such a complete history could even be conceived. That Dickson was able to accomplish such a feat is attested to by the fact that his History has become the standard reference for number theory up to that time. One need only look at later classics, such as Hardy and Wright, where Dickson's History is frequently cited, to see its importance. The book is divided into three volumes by topic. In scope, the coverage is encyclopedic, leaving very little out. It is interesting to see the topics being resuscitated today that are treated in detail in Dickson. The first volume of Dickson's History covers the related topics of divisibility and primality. It begins with a description of the development of our understanding of perfect numbers. Other standard topics, such as Fermat's theorems, primitive roots, counting divisors, the Möbius function, and prime numbers themselves are treated. Dickson, in this thoroughness, also includes less workhorse subjects, such as methods of factoring, divisibility of factorials and properties of the digits of numbers. Concepts, results and citations are numerous. This second volume is a comprehensive treatment of Diophantine analysis. Besides the familiar cases of Diophantine equations, this rubric also covers partitions, representations as a sum of two, three, four or $n$ squares, Waring's problem in general and Hilbert's solution of it, and perfect squares in artihmetical and geometrical progressions. Of course, many important Diophantine equations, such as Pell's equation, and classes of equations, such as quadratic, cubic and quartic equations, are treated in detail. As usual with Dickson, the account is encyclopedic and the references are numerous. The last volume of Dickson's History is the most modern, covering quadratic and higher forms. The treatment here is more general than in Volume II, which, in a sense, is more concerned with special cases. Indeed, this volume chiefly presents methods of attacking whole classes of problems. Again, Dickson is exhaustive with references and citations.