Diophantine Equations Over Function Fields
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Diophantine Equations Over Function Fields
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Author : R. C. Mason
language : en
Publisher: Cambridge University Press
Release Date : 1984-04-26
Diophantine Equations Over Function Fields written by R. C. Mason 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 1984-04-26 with Mathematics categories.
A self-contained account of a new approach to the subject.
Diophantine Equations Over Function Fields
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Author : R. C. Mason
language : en
Publisher:
Release Date : 2014-05-14
Diophantine Equations Over Function Fields written by R. C. Mason and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
A self-contained account of a new approach to the subject.
Diophantine Equations Over Function Fields
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Author : R. C. Mason
language : en
Publisher: Cambridge University Press
Release Date : 1984-04-26
Diophantine Equations Over Function Fields written by R. C. Mason 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 1984-04-26 with Mathematics categories.
Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate.
Effective Results And Methods For Diophantine Equations Over Finitely Generated Domains
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Author : Jan-Hendrik Evertse
language : en
Publisher: Cambridge University Press
Release Date : 2022-04-28
Effective Results And Methods For Diophantine Equations Over Finitely Generated Domains written by Jan-Hendrik Evertse 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 2022-04-28 with Mathematics categories.
Provides exceptional coverage of effective solutions for Diophantine equations over finitely generated domains.
Function Field Arithmetic
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Author : Dinesh S Thakur
language : en
Publisher: World Scientific
Release Date : 2004-06-01
Function Field Arithmetic written by Dinesh S Thakur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-01 with Mathematics categories.
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
Function Field Arithmetic
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Author : Dinesh S. Thakur
language : en
Publisher: World Scientific
Release Date : 2004
Function Field Arithmetic written by Dinesh S. Thakur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
My Numbers My Friends
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Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-10
My Numbers My Friends written by Paulo Ribenboim 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 2006-05-10 with Mathematics categories.
This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly accessible to everyone with an interest in numbers. This new collection includes essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as Kummers work on Fermat's last theorem.
Analytic Number Theory
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Author : B. Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analytic Number Theory written by B. Berndt 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 2012-12-06 with Mathematics categories.
On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.
Analysis At Urbana Analysis In Function Spaces
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Author : Earl Berkson
language : en
Publisher: CUP Archive
Release Date : 1989
Analysis At Urbana Analysis In Function Spaces written by Earl Berkson and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Throughout the academic year 1986-7, the University of Illinois hosted a symposium on mathematical analysis attended by some of the leading figures in the field. This resulting book lays emphasis on the synthesis of modern and classical analysis.
Arithmetical Functions
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Author : Wolfgang Schwarz
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-10
Arithmetical Functions written by Wolfgang Schwarz 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 1994-03-10 with Mathematics categories.
Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis.