Diophantine Analysis And Related Fields 2010
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Diophantine Analysis And Related Fields 2010
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Author : Takao Komatsu
language : en
Publisher: American Institute of Physics
Release Date : 2010-08-13
Diophantine Analysis And Related Fields 2010 written by Takao Komatsu and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-13 with Mathematics categories.
The purpose of the conference was to report recent progress and developments of diophantine aspects of analytic number theory, especially focusing upon the topics in diophantine analysis and related fields; its simultaneous objectives are to promote interactions between analytic number theorists and mathematicians from other fields, and further to create opportunities for opening up new individual/collaborative research projects.
Diophantine Analysis And Related Fields
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Author : Takao Komatsu
language : en
Publisher: American Institute of Physics
Release Date : 2008-02-05
Diophantine Analysis And Related Fields written by Takao Komatsu and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-05 with Mathematics categories.
"This volume consists of contributions presented by participants at both the Diophantine Analysis and Related Fields 2007 (DARF 2007) conference held at Keio University, Yokohama, Japan, from March 7 to 9, 2007 and the upcoming Diophantine Analysis and Related Fields 2008 (DARF 2008) conference to be held at Doshisha University, Kyoto, Japan, from March 5 to 7, 2008."--Pref.
Lecture Notes On Diophantine Analysis
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Author : Umberto Zannier
language : en
Publisher: Springer
Release Date : 2015-05-05
Lecture Notes On Diophantine Analysis written by Umberto Zannier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-05 with Mathematics categories.
These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Exploring The Number Jungle
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Author : Edward B. Burger
language : en
Publisher: American Mathematical Soc.
Release Date :
Exploring The Number Jungle written by Edward B. Burger 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 with Mathematics categories.
The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory."--BOOK JACKET.
Elliptic Curves
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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Elliptic Curves written by S. Lang 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 2013-06-29 with Mathematics categories.
It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.
Fundamentals Of Diophantine Geometry
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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fundamentals Of Diophantine Geometry written by S. Lang 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 2013-06-29 with Mathematics categories.
Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.
Number Theory And Related Fields
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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-16
Number Theory And Related Fields written by Jonathan M. Borwein 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 2013-05-16 with Mathematics categories.
“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.
Recent Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Birkhäuser
Release Date : 2017-08-23
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Publications Math Matiques De Besan On N 1 2010
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Author : Patrick Hild
language : en
Publisher: Presses Univ. Franche-Comté
Release Date : 2010-03
Publications Math Matiques De Besan On N 1 2010 written by Patrick Hild and has been published by Presses Univ. Franche-Comté this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03 with categories.
Number Theory
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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-17
Number Theory written by Henri Cohen 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 2008-12-17 with Mathematics categories.
This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.