Download or read book Prehomogeneous vector spaces and field extensions written by David J. Wright and published by . This book was released on 1991 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Prehomogeneous Vector Spaces written by Tatsuo Kimura and published by American Mathematical Soc.. This book was released on 2003 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory. An important objective is to create applications to number theory. For example, one of the key topics is that of zeta functions attached to prehomogeneous vector spaces; these are generalizations of the Riemann zeta function, a cornerstone of analytic number theory. Prehomogeneous vector spaces are also of use in representation theory, algebraic geometry and invariant theory. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces. It strives, and to a large extent succeeds, in making this content, which is by its nature fairly technical, self-contained and accessible. The first section of the book, "Overview of the theory and contents of this book," Is particularly noteworthy as an excellent introduction to the subject.
Download or read book Prehemogeneous Vector Spaces and Field Extensions written by D. J. Wright and published by . This book was released on 1991 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Enumeration in Vector Spaces Over a Field Extension written by Patrick Francois Rabau and published by . This book was released on 1988 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithmic Number Theory written by Claus Fieker and published by Springer. This book was released on 2003-08-02 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Algorithmic Number Theory Symposium, ANTS-V, held in Sydney, Australia, in July 2002. The 34 revised full papers presented together with 5 invited papers have gone through a thorough round of reviewing, selection and revision. The papers are organized in topical sections on number theory, arithmetic geometry, elliptic curves and CM, point counting, cryptography, function fields, discrete logarithms and factoring, Groebner bases, and complexity.
Download or read book Algorithmic Number Theory written by Wieb Bosma and published by Springer. This book was released on 2006-12-30 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.
Download or read book Shintani Zeta Functions written by Akihiko Yukie and published by . This book was released on 1993 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory.
Download or read book Advanced Topics in Computational Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2012-10-29 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Download or read book Shintani Zeta Functions written by Akihiko Yukie and published by Cambridge University Press. This book was released on 1993 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is amongst the first books on the theory of prehomogeneous vector spaces, and represents the author's deep study of the subject.
Download or read book Finite Dimensional Vector Spaces written by Paul R. Halmos and published by Princeton University Press. This book was released on 1947-01-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."
Download or read book Algorithmic Number Theory written by and published by . This book was released on 2002 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Vector Spaces written by Lawrence Narici and published by CRC Press. This book was released on 2010-07-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller and published by Springer. This book was released on 2016-09-20 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Download or read book written by and published by . This book was released on 2000 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extension Theorems in Vector Spaces Over Finite Fields written by Doowon Koh and published by . This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the L[superscript p] - L[superscript r] boundedness of the extension operator associated with algebraic varieties such as nondegenerate quadratic surfaces, paraboloids, and cones in vector spaces over finite fields. We obtain the best possible result for the extension theorems related to nondegenerate quadratic curves in two dimensional vector spaces over finite fields. In higher even dimensions, we improve upon the Tomas-Stein exponents which were obtained by Mockenhaupt and Tao ([21]) by studying extension theorems for paraboloids in the finite field setting. We also study extension theorems for cones in vector spaces over finite fields. We give an alternative proof of the best possible result for the extension theorems for cones in three dimensions, which originally is due to Mockenhaupt and Tao ([21]). Moreover, our method enables us to obtain the sharp L2 - L[superscript r] estimate of the extension operator for cones in higher dimensions. In addition, we study the relation between extension theorems for spheres and the Erdos-Falconer distance problems in the finite field setting. Using the sharp extension theorem for circles, we improve upon the best known result, due to A. Iosevich and M. Rudnev ([17]), for the Erdos-Falconer distance problems in two dimensional vector spaces over finite fields. Discrete Fourier analytic machinery, arithmetic considerations, and classical exponential sums play an important role in the proofs.
Download or read book Combinatorial Number Theory written by Bruce Landman and published by Walter de Gruyter. This book was released on 2013-08-29 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.
Download or read book Representation Theory Complex Analysis and Integral Geometry written by Bernhard Krötz and published by Springer Science & Business Media. This book was released on 2011-12-14 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
