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Monday, July 27, 2020 | History

3 edition of Diophantine equations and inequalities in algebraic number fields found in the catalog.

Diophantine equations and inequalities in algebraic number fields

Wang, Yuan

Diophantine equations and inequalities in algebraic number fields

by Wang, Yuan

  • 294 Want to read
  • 35 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Algebraic fields.,
  • Diophantine analysis.,
  • Inequalities (Mathematics)

  • Edition Notes

    Includes bibliographical references (p. 163-167) and index.

    StatementWang Yuan.
    Classifications
    LC ClassificationsQA247 .W345 1991
    The Physical Object
    Paginationxvi, 168 p. ;
    Number of Pages168
    ID Numbers
    Open LibraryOL1865924M
    ISBN 103540520198, 0387520198
    LC Control Number90023989

    This text includes an extended abstract of a keynote talk under the title Families of Thue equations associated with a rank one subgroup of the unit group of a number field given on September 4. $\begingroup$ Pierre Samuel's "Algebraic Theory of Numbers" gives a very elegant introduction to algebraic number theory. It doesn't cover as much material as many of the books mentioned here, but has the advantages of being only pages or so and being published by .

    H., Davenport, Analytic Methods for Diophantine Equations and Diophantine Inequalities (Campus Publications, ; Cambridge Mathematical Library, 2nd revised edn prepared by T. D. Browning, Cambridge University Press, ). FindInstance [expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex. FindInstance [expr, vars, Integers] finds solutions to Diophantine equations. FindInstance [expr, vars, Booleans] solves Boolean satisfiability for expr.

    The book is almost self-contained: The first part, chapters 1, 2 and 3, gives a quick summary of the basic facts on algebraic number theory (traces, norms, discriminants, absolute values and places, rings of integers, \(S\)-integers, units and heights), algebraic function fields, and some results from Diophantine analysis. The second part is. This book presents methods of solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular, divisibility and diophantine equations. While this book emphasizes some methods that are not usually covered in beginning.


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Diophantine equations and inequalities in algebraic number fields by Wang, Yuan Download PDF EPUB FB2

Diophantine Equations and Inequalities in Algebraic Number Fields. Authors (view affiliations) Wang Yuan; Book. 1 Search within book. Front Matter. Pages I-XVI. PDF. The Circle Method and Waring’s Problem method Diophantische Gleichung Kreismethode Waring's problem Waring`s problem Waringsches Problem algebraic number field.

Buy Diophantine Equations and Inequalities in Algebraic Number Fields on FREE SHIPPING on qualified orders Diophantine Equations and Inequalities in Algebraic Number Fields: Wang, Yuan: : BooksCited by: 8.

Diophantine Equations and Inequalities in Algebraic Number Fields. Authors: Wang, Yuan Free Preview. Diophantine Equations and Inequalities in Algebraic Number Fields | Prof.

Wang Yuan (auth.) | Diophantine equations and inequalities in algebraic number fields book | B–OK. Download books for free. Find books.

Wang gives generalizations of important results on diophantine equations and inequalities over rational fields to algebraic number fields. He also offers an account of Siegal's generalized circle method and its applications to Waring's problem and additive equations and an Author: Jan-Hendrik Evertse.

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed.

The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine s: 4. ax + by = 1: This is a linear Diophantine equation.

w 3 + x 3 = y 3 + z 3: The smallest nontrivial solution in positive integers is 12 3 + 1 3 = 9 3 + 10 3 = It was famously given as an evident property ofa taxicab number (also named Hardy–Ramanujan number) by Ramanujan to Hardy while meeting in There are infinitely many nontrivial solutions.

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations.

This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training.

It can also be used as a source of supplementary material for any course dealing with algebraic equations or inequalities, or to supplement a standard elementary number theory course.5/5(1).

Diophantine geometry and, more generally, arithmetic geometry is the study of the points of an algebraic variety with coordinates in fields that are not algebraically closed and occur in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields.

Diophantine equations and inequalities in algebraic number fields. Berlin ; New York: Springer-Verlag, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Yuan Wang. Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry.

This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated.

Cite this chapter as: Yuan W. () Diophantine Inequalities for Forms. In: Diophantine Equations and Inequalities in Algebraic Number Fields.

The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book.

This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and. 16 hours ago  In the accepted answer, several concepts like Euler product, class number, regulator of algebraic number field, number of roots of unity contained in imaginary quadratic number field etc.

I am familiar with basic number theory, but such higher level knowledge is beyond my scope. I am not sure if this is the right place to ask such question. Basic algebraic number theory; 2. Algebraic function fields; 3. Tools from Diophantine approximation and transcendence theory; Part II.

Unit equations and applications: 4. Effective results for unit equations in two unknowns over number fields; 5. Algorithmic resolution of unit equations in two unknowns; 6. Unit equations in several unknowns; 7. Get this from a library. Diophantine Equations and Inequalities in Algebraic Number Fields.

[Wang Yuan] -- The circle method has its genesis in a paper of Hardy and. Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role.

This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields. Comments. The most outstanding recent result in the study of Diophantine equations was the proof by G.

Falting of the Mordell conjecture, stating that curves of genus $ > 1 $(cf. Genus of a curve) over algebraic fields have no more than a finite number of rational points (cf.).From this result it follows, in particular, that the Fermat equation $ x ^ {n} + y ^ {n} + z ^ {n} = 0 $ has only a.

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.

Buy Unit Equations in Diophantine Number Theory (Cambridge Studies in Advanced Mathematics) UK ed. by Evertse, Jan-Hendrik, Győry, Kálmán (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible orders.Diophantine equations and diophantine inequalities in algebraic number fields, Cont. Math; 77, AMS,On small zeros of quadratic forms over finite fields, J. of number theory, 31,On a generalized Waring's problem in algebraic number fields, in ``Number Theory'' in honor of Loo Keng Hua, Springer--Verlag, This undergraduate textbook, suitable for first year students, introduces the reader to number theory and abstract algebra.

Many topics are covered such as sums of squares, Hilbert's hotel, Diophantine equations, Gaussian integers, and quadratic reciprocity. exercises, including programming.