Lattice Points
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Area Lattice Points And Exponential Sums
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Author : M. N. Huxley
language : en
Publisher: Clarendon Press
Release Date : 1996-06-13
Area Lattice Points And Exponential Sums written by M. N. Huxley and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-13 with Mathematics categories.
In analytic number theory a large number of problems can be "reduced" to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput's method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background.
Lattice Points
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Author : Ekkehard Krätzel
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-03-31
Lattice Points written by Ekkehard Krätzel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-31 with Mathematics categories.
This book is devoted to a special problem of number theory, that is the estimation of the number of lattice points in large closed domains of ordinary Euclidean spaces. Circle and sphere problems, Dirichlet's divisor problem, the distribution of powerful numbers, and finite Abelian groups are also investigated. The object of this book is to acquaint the reader with the fundamental results and methods, so that follow up with the original papers is possible.
Lattice Point Identities And Shannon Type Sampling
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2019-10-28
Lattice Point Identities And Shannon Type Sampling written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-28 with Technology & Engineering categories.
Lattice Point Identities and Shannon-Type Sampling demonstrates that significant roots of many recent facets of Shannon's sampling theorem for multivariate signals rest on basic number-theoretic results. This book leads the reader through a research excursion, beginning from the Gaussian circle problem of the early nineteenth century, via the classical Hardy-Landau lattice point identity and the Hardy conjecture of the first half of the twentieth century, and the Shannon sampling theorem (its variants, generalizations and the fascinating stories about the cardinal series) of the second half of the twentieth century. The authors demonstrate how all these facets have resulted in new multivariate extensions of lattice point identities and Shannon-type sampling procedures of high practical applicability, thereby also providing a general reproducing kernel Hilbert space structure of an associated Paley-Wiener theory over (potato-like) bounded regions (cf. the cover illustration of the geoid), as well as the whole Euclidean space. All in all, the context of this book represents the fruits of cross-fertilization of various subjects, namely elliptic partial differential equations, Fourier inversion theory, constructive approximation involving Euler and Poisson summation formulas, inverse problems reflecting the multivariate antenna problem, and aspects of analytic and geometric number theory. Features: New convergence criteria for alternating series in multi-dimensional analysis Self-contained development of lattice point identities of analytic number theory Innovative lattice point approach to Shannon sampling theory Useful for students of multivariate constructive approximation, and indeed anyone interested in the applicability of signal processing to inverse problems.
The Geometry Of Numbers
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Author : C. D. Olds
language : en
Publisher: Cambridge University Press
Release Date : 2000
The Geometry Of Numbers written by C. D. Olds and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
A self-contained introduction to the geometry of numbers.
Metaharmonic Lattice Point Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2011-05-09
Metaharmonic Lattice Point Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-09 with Mathematics categories.
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of
Introduction To Crystallography
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Author : Donald E. Sands
language : en
Publisher: Courier Corporation
Release Date : 2012-06-14
Introduction To Crystallography written by Donald E. Sands and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Science categories.
Clear, concise explanation of logical development of basic crystallographic concepts. Topics include crystals and lattices, symmetry, x-ray diffraction, and more. Problems, with answers. 114 illustrations. 1969 edition.
Topics In The Theory Of Numbers
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Author : Janos Suranyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-14
Topics In The Theory Of Numbers written by Janos Suranyi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-14 with Mathematics categories.
Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.
Integer Points In Polyhedra Geometry Number Theory Representation Theory Algebra Optimization Statistics
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Author : Matthias Beck
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Integer Points In Polyhedra Geometry Number Theory Representation Theory Algebra Optimization Statistics written by Matthias Beck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"The AMS-IMS-SIAM Joint Summer Research Conference "Integer Points in Polyhedra--Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics" was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference. The volume is a cross section of recent advances connected to lattice-point questions. Similar to the talks given at the conference, topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields." -- Back cover.
Advanced Number Theory
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Author : Harvey Cohn
language : en
Publisher: Courier Corporation
Release Date : 1980-08-01
Advanced Number Theory written by Harvey Cohn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-08-01 with Mathematics categories.
"A very stimulating book ... in a class by itself." — American Mathematical Monthly Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject. The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups. Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints. In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory.
Single Crystal Neutron Diffraction From Molecular Materials
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Author : Chick C. Wilson
language : en
Publisher: World Scientific
Release Date : 2000
Single Crystal Neutron Diffraction From Molecular Materials written by Chick C. Wilson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
This important book presents a comprehensive account of the techniques & applications of single crystal neutron diffraction in the area of chemical crystallography & molecular structure. Beginning with a brief description of the general principles & the reasons for choosing the technique - the "why" - the book covers the methods for both the production of neutrons & the measurement of their scattering by molecular crystals - the "how" - followed by a detailed survey of past, present & future applications - the "what". The coverage of both steady state & pulsed neutron sources & instrumentation is extensive, while the survey of applications is the most comprehensive yet undertaken. The book endeavours to show why the technique is an essential method for studying areas as diverse as hydrogen bonding & weak interactions, organometallics, supramolecular chemistry & crystal engineering, metal hydrides, charge density & pharmaceuticals. It is an ideal reference source for the research worker interested in using neutron diffraction to study the structure of molecules. Contents: Crystallography & the Importance of Structural Information; Neutron Scattering; Neutron Diffractometers; Review of Applications I: The Accurate Location of Atoms; Review of Applications II: Hydrogen Bonding & Other Intermolecular Interactions; Review of Applications III: Probing Vibrations & Disorder; Impact on Material Properties & Design; The Future: New Instruments, New Sources, New Techniques. Readership: Students & researchers involved in structural science, especially chemical crystallography.