Algorithmics Of Lattices In Euclidean Spaces With Application To Computations With Siegel Modular Forms
Download Algorithmics Of Lattices In Euclidean Spaces With Application To Computations With Siegel Modular Forms full books in PDF, epub, and Kindle. Read online free Algorithmics Of Lattices In Euclidean Spaces With Application To Computations With Siegel Modular Forms ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : William A. Stein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 290 |
| Release | : 2007-02-13 |
| Genre | : Mathematics |
| ISBN | : 0821839608 |
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
| Author | : Phong Q. Nguyen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 503 |
| Release | : 2009-12-02 |
| Genre | : Computers |
| ISBN | : 3642022952 |
The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.
| Author | : Matthias Beck |
| Publisher | : Springer |
| Total Pages | : 295 |
| Release | : 2015-11-14 |
| Genre | : Mathematics |
| ISBN | : 1493929690 |
This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
| Author | : Jan Hendrik Bruinier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2008-02-10 |
| Genre | : Mathematics |
| ISBN | : 3540741194 |
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
| Author | : Chee-Keng Yap |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 511 |
| Release | : 2000 |
| Genre | : Computers |
| ISBN | : 9780195125160 |
Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students
| Author | : Steven Galbraith |
| Publisher | : |
| Total Pages | : |
| Release | : 2020-12-29 |
| Genre | : |
| ISBN | : 9781935107071 |
The Algorithmic Number Theory Symposium (ANTS), held biennially since 1994, is the premier international forum for research in computational and algorithmic number theory. ANTS is devoted to algorithmic aspects of number theory, including elementary, algebraic, and analytic number theory, the geometry of numbers, arithmetic algebraic geometry, the theory of finite fields, and cryptography.This volume is the proceedings of the fourteenth ANTS meeting, which took place 29 June to 4 July 2020 via video conference, the plans for holding it at the University of Auckland, New Zealand, having been disrupted by the COVID-19 pandemic. The volume contains revised and edited versions of 24 refereed papers and one invited paper presented at the conference.
| Author | : C. D. Olds |
| Publisher | : Cambridge University Press |
| Total Pages | : 198 |
| Release | : 2001-02-22 |
| Genre | : Mathematics |
| ISBN | : 9780883856437 |
A self-contained introduction to the geometry of numbers.
| Author | : Henri Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 556 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662029456 |
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
| Author | : J.H. Conway |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 724 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475722494 |
The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.
| Author | : |
| Publisher | : |
| Total Pages | : 1852 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : |
