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Topic: Diophantine analysis

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	Untitled Document (Site not responding. Last check: 2007-11-02)
		Diophantine analysis is a branch of number theory.
		A few other problems that are examples of Diophantine analysis would be: find two integers such that the sum of their squares is a square, two integers such that the sum of their cubes is a square, or three integers such that their squares are in arithmetic progression.
		Diophantine analysis was easier to understand than the Inca's calendar, the last project I did.
	www.ga.k12.pa.us /academics/MS/8th/haddad/Alicia/body.htm (263 words)

	diophanfin.html
		Diophantine equations are equations of polynomial expressions for which rational or integer solutions are sought.
		For Diophantine equations of the type ax+by=c, there exists an infinite number of solutions if (a,b)c, that is if the greatest common divisor of a and b divides c.
		These examples of Diophantine contributions are sufficient to show that his works have helped shape the world in which we live.
	www.ms.uky.edu /~carl/ma330/projects/diophanfin1.html (2434 words)

	[No title]
		Other types of Diophantine problems with (partial) solutions The basic setting for Diophantine problems is a set of equations which are to be solved in whole numbers (or in some cases rational numbers or numbers of a certain form).
		In section III we consider separately the general families of Diophantine problems which have solutions or which are amenable to attack by some established procedures.
		Others important Diophantine questions involve the sum-of-divisors function sigma --- for example, solutions to the equation sigma(n)=2n are the perfect numbers; solutions to the pair of equations sigma(n)=2m, sigma(m)=2n are the amicable numbers.
	www.math.niu.edu /~rusin/known-math/98/diophantine (4373 words)

	Metrical Diophantine Analysis For Tame Parabolic Iterated Function Systems - Stratmann, Urba (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		The second goal is to provide a metrical Diophantine analysis for these parabolic limit sets in the spirit of theorems of...
		1.1: Jarník and Julia; a Diophantine analysis for..
		4 Jarn'ik and Julia; a Diophantine analysis for parabolic rati..
	citeseer.ist.psu.edu /328820.html (521 words)

	Diophantus and Diophantine Equations - Cambridge University Press
		This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since.
		The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat.
		Diophantine equations in the works of Euler and Jacobi: addition of points on an elliptic curve; 11.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0883855267 (234 words)

	CRC Press Online (Site not responding. Last check: 2007-11-02)
		While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory.
		Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects.
		Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field.
	crcpress.co.uk /shopping_cart/products/product_detail.asp?sku=C4827&... (379 words)

	The Diophantine Analysis Of Conformal Iterated Function Systems (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		Introduction, Preliminaries The diophantine analysis has its origins in classical papers [Be] and [Ja] by Besicovic and Jarnik respectively.
		0.7: Jarník and Julia; a Diophantine analysis for..
		4 Jarnik and Julia; a Diophantine analysis for parabolic ratio..
	citeseer.ist.psu.edu /218526.html (396 words)

	Diophantine Analysis - Search Results - MSN Encarta (Site not responding. Last check: 2007-11-02)
		Diophantine Analysis - Search Results - MSN Encarta
		Diophantine Analysis, in mathematics, branch of number theory concerned with determining the solutions in integers of algebraic equations with two...
		Diophantine equations are equations in one or more unknowns and integral coefficients, for which integral solutions are sought (Diophantine Analysis;...
	uk.encarta.msn.com /Diophantine_Analysis.html (103 words)

	Amazon.com: Diophantine Analysis: Books: V. I. Bernik,M. M. Dodson,M.M. Dodson (Site not responding. Last check: 2007-11-02)
		Dodson, M.M. Dodson "Diophantine approximation is a more quantitative and general study of the density of the rationals Q in the reals R while a smooth manifold is..." (more)
		This volume explores Diophantine approximation on smooth manifolds embedded in Euclidean space, developing a coherent body of theory comparable to that of classical Diophantine approximation.
		Diophantine approximation is a more quantitative and general study of the density of the rationals Q in the reals R while a smooth manifold is locally diffeomorphic to Euclidean space.
	www.amazon.com /Diophantine-Analysis-V-I-Bernik/dp/0521432758 (744 words)

	Diophantine Analysis: Proceedings Of The Number Theory Section Of The 1985 Australian Mathematical Society Convention; ... (Site not responding. Last check: 2007-11-02)
		Diophantine Analysis: Proceedings Of The Number Theory Section Of The 1985 Australian Mathematical Society Convention; Author: Australian Mathematical Society; Paperback
		Diophantine Analysis: Proceedings Of The Number Theory Section Of The 1985 Australian Mathematical Society Convention
		They survey recent work in Diophantine analysis.These papers were presented at the 1985 Australian Mathematical Society convention.
	www.netstoreusa.com /mabooks/052/0521339235.shtml (206 words)

	Read This: Exploring the Number Jungle
		Whatever differences one finds between books have to do with details of approach and style or with what is done in the more advanced chapters, after the obligatory chapters dealing with divisibility, congruences, linear diophantine equations, primitive roots, and quadratic reciprocity.
		The chapters, actually called "modules," typically end with "Big Picture Questions" which invite the student to attempt to consider what has been done so far, where it might be going, and why it is interesting.
		For the first ten modules, the focus is on approximating irrational numbers by rationals while controlling the size of the denominator of the approximants.
	www.maa.org /reviews/numjungle.html (964 words)

	OUP: UK General Catalogue
		Welcome to diophantine analysis--an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers.
		Diophantine analysis comprises two different but interconnected domains--diophantine approximation and diophantine equations.
		This highly readable book brings to life the fundamental ideas and theorems from diophantine approximation, geometry of numbers, diophantine geometry and $p$-adic analysis.
	www.oup.com /uk/catalogue/?ci=9780821826409 (454 words)

	Diophantine Equation--2nd Powers -- from Wolfram MathWorld
		Solution to the general bivariate quadratic Diophantine equation is implemented as
		For quadratic Diophantine equations in more than two variables, there exist additional deep results due to C. Siegel.
		Nagell, T. "Diophantine Equations of the Second Degree." Ch.
	mathworld.wolfram.com /DiophantineEquation2ndPowers.html (672 words)

	Rowan University Course Catalog
		This course includes divisibility properties of integers, mathematical induction, modular congruence, linear congruences and diophantine analysis, congruences of higher degree, quadratic residues, famous problems of number theory.
		The continuation of Real Analysis I covering Riemann-Stieltjes integration, sequences and series of function, functions of several variables, elements of measure theory and Lebesgue integration.
		The continuation of Complex Analysis I covering Riemann-Stieltjes integration, meromorphic functions, conformal mappings, analytic continuation, fractional linear transformations and periodic functions.
	www.rowan.edu /catalogs/grad/courses/?dnum=1701 (835 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		A simple linear transformation of the biquaternionic parameters {alpha} and {beta} of the group SL(2, C), which is two-to-one homomorphic to the restricted Lorentz group L, is used to express each element of SL(2, C) and L in terms of the first column of an element of L and the quaternionic parameters {alpha}.
		This parametrization is shown to bring the determination of the integral realizations of the restricted Lorentz group under the purview of classical Diophantine analysis, involving the expression of a given pair of integers, respectively, as a sum of three squares and a sum of four squares.
		These solutions are further constrained by the condition that a set of four integers, which is linear in the solution of the three squares problem and in the solution of the four squares problem, have a common factor.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20420015 (359 words)

	Diophantine Equation -- from Wolfram MathWorld
		A Diophantine equation is an equation in which only integer solutions are allowed.
		Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution.
		A linear Diophantine equation (in two variables) is an equation of the general form
	mathworld.wolfram.com /DiophantineEquation.html (616 words)

	EQUATION (from Lat. ae... - Online Information article about EQUATION (from Lat. ae...
		analysis was extensively studied by Diophantus, and is sometimes termed the Diophantine Analysis.
		Indeterminate problems are of different orders, according to the dimensions of the equation which is obtained after all the unknown quantities but two have been eliminated by means of the given equations.
		The process as to the point D', translated into analysis, is the ordinate process of See also:
	encyclopedia.jrank.org /EMS_EUD/EQUATION_from_Lat_aequatio_aequ.html (11145 words)

	CANT 2006
		Moreover the use of combinatorics is sought in the analysis of algorithms, initiated by D.~E.~Knuth, and which greatly relies on number theory, asymptotic methods and computer algebra [6,8,12].
		Other examples are given by the study of digital functions, automatic sequences and the transcendence of formal power series, the Rauzy fractal and discrepancy problems and by the representation of real numbers in various numeration systems [2,5].
		This latter problem is in particular related to Diophantine analysis or approximations of real numbers to algebraic numbers, which has recently enjoyed striking developments through a fruitful interplay between Diophantine approximation and combinatorics on words [1,15].
	www.cant2006.ulg.ac.be /scope.html (845 words)

	Diophantine Analysis - Wal-Mart
		Diophantine analysis is an extremely active field in number theory because of its many open problems and conjectures.
		Requiring only a basic understanding of number theory, Diophantine Analysis is built around the detailed theory of continued fractions and features many applications and examples.
		The author includes many new topics related to discrete mathematics, such as factoring large integers, error-free computing, and factoring polynomials.
	www.walmart.com /catalog/product.gsp?product_id=3577816 (535 words)

	The Theory of Numbers and Diophantine Analysis
		Diophantine Analysis is organized around the notion of a multiplicative domain and covers rational triangles; method of infinite descent; problems involving a multiplicative domain; equations of the third, fourth, and higher degree; the Fermat problem; and the method of functional equations.
		Theoretical Numerical Analysis: An Introduction to Advanced Techniques
		Concise text focuses on fundamentals of functional analysis and approximation theory, the major results of theoretical numerical analysis; and specific topics that illustrate the power and usefulness of theoretical analysis.
	store.doverpublications.com /0486438031.html (178 words)

	Diophantine Analysis - Cambridge University Press
		The papers in this volume, which were presented at the 1985 Australian Mathematical Society convention, survey recent work in Diophantine analysis.
		The contributors are leading mathematicians in the world, and their articles are state of the art accounts, many of which include open problems pointing the way to further research.
		The contributions will be of general interest to number theorists and of particular interest to workers in transcendence theory, Diophantine approximation and exponential sums.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521339235 (229 words)

	History of the Theory of Numbers, Volume ll: Diophantine Analysis
		This second volume in the series History of the Theory of Numbers presents twenty-six chapters of material related to Diophantine Analysis.
		At the end of the volume is a separate subject and author index.
		Single-volume compilation of two complete works: The Theory of Numbers explores prime numbers, elementary properties of congruences, the theories of Fermat and Wilson, primitive roots modulo m, and other topics; Diophantine Analysis covers rational triangles, me...
	store.doverpublications.com /0486442330.html (382 words)

	Math Games:Beautiful References
		Vol 2, Diophantine Analysis, covers right triangles, sums of powers, and Fermat's last theorem.
		I personally found advanced Analysis brutally difficult — I doubt I'd have gotten through the following text without lots of good instruction from my professor, Rinaldo Schinazi.
		Reference 16: Principles of Mathematical Analysis, by Walter Rudin.
	www.maa.org /editorial/mathgames/mathgames_01_02_06.html (3237 words)

	DC MetaData for: Jarn\'{\i}k and Julia; a Diophantine Analysis for Parabolic Rational Maps
		DC MetaData for: Jarn\'{\i}k and Julia; a Diophantine Analysis for Parabolic Rational Maps
		Jarn\'{\i}k and Julia; a Diophantine Analysis for Parabolic Rational Maps
		Abstract: In this paper we derive a Diophantine analysis
	www.uni-math.gwdg.de /preprint/meta/mg.1999.02.html (69 words)

	Publications - Department of Mathematics - University of York
		Victor Beresnevich, H. Dickinson, Sanju Velani, Diophantine approximation on planar curves and the distribution of rational points (with an appendix by R.C. Vaughan: Sums of two squares near perfect squares), Annals of Math.
		Victor Beresnevich, E. Kovalevskaya, On Diophantine approximations of dependent quantities in the p-adic case, Mat.
		G.Â A.Â Margulis, Victor Beresnevich, Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate manifolds, Mosc.
	maths.york.ac.uk /www/ResearchPublications (9560 words)

	Conference I. SHIOKAWA (Site not responding. Last check: 2007-11-02)
		The conference on Diophantine Analysis and Related Fields 2006 will take place, which is sponsored by Japan Society for the Promotion of Science (Grant-in-Aid for Scientifc Research, Nos.~15540021;~16540038), by Keio University (Academic Research Promotion Funds and Economics Faculty Fund), as well as by Fund for the Promotion of International Scientific Research (Grant B-1, 2005).
		The conference aims 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.
		The conference will be held in honor of Professor Iekata Shiokawa on the occasion of his retirement from Keio University.
	mathweb.sc.niigata-u.ac.jp /ant/Sympo/dioph06_e.html (225 words)

	Table of contents for Library of Congress control number 97074342
		Table of contents for Diophantus and diophantine equations / I.G. Bashmakova; updated by Joseph Silverman ; translated from the Russian by Abe Shenitzer with the editorial assistance of Hardy Grant.
		Bibliographic record and links to related information available from the Library of Congress catalog
		Library of Congress subject headings for this publication: Diophantine analysis
	www.loc.gov /catdir/toc/cam026/97074342.html (139 words)

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