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Author: Harold Davenport Publisher: ISBN: Category : Mathematics Languages : en Pages : 602
Book Description
In this volume are collected Davenport's papers on Waring's problem, and on forms in many variables. The comments at the ends of some papers includes information on how some papers came to be written, but rather few technical comments. The mathematical works speak for themselves.
Author: Harold Davenport Publisher: ISBN: Category : Mathematics Languages : en Pages : 602
Book Description
In this volume are collected Davenport's papers on Waring's problem, and on forms in many variables. The comments at the ends of some papers includes information on how some papers came to be written, but rather few technical comments. The mathematical works speak for themselves.
Author: A. Schinzel Publisher: Cambridge University Press ISBN: 9781139426718 Category : Mathematics Languages : en Pages : 590
Book Description
This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.
Author: Alexander Schrijver Publisher: John Wiley & Sons ISBN: 9780471982326 Category : Mathematics Languages : en Pages : 488
Book Description
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
Author: Harold Davenport Publisher: ISBN: Category : Mathematics Languages : en Pages : 458
Book Description
These volumes contain the collected mathematical papers of H. Davenport. Volume II contains a great many of the papers on Diophantine approximation and the geometry of numbers. The mathematical works speak for themselves.
Author: Nicholas M. Katz Publisher: Princeton University Press ISBN: 0691153310 Category : Mathematics Languages : en Pages : 212
Book Description
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Author: Harold Davenport
Author: Harold Davenport
Author: Harold Davenport
Author: A. Schinzel
Author: Alexander Schrijver
Author: Harold Davenport
Author: Alan Baker
Author: Nicholas M. Katz
Author: Marvin I. Knopp
Author: British Library
Author: