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Analytic Methods for Diophantine Equations and Diophantine Inequalitiesby H. Davenport; T. D. Browning
Cambridge University Press 2005; US$ 51.00Harold 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 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. more...
Heights in Diophantine Geometryby Enrico Bombieri; Walter Gubler; Bela Bollobas; William Fulton; Anatole Katok; Frances Kirwan; Peter Sarnak; Barry Simon
Cambridge University Press 2006; US$ 78.00Diophantine geometry has been studied by number theorists for thousands of years, this monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. more...
Hilbert's Tenth Problemby Alexandra Shlapentokh
Cambridge University Press 2006; US$ 118.00Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields. more...
Linear Algebra, Rational Approximation and Orthogonal Polynomialsby A. Bultheel; M. Van Barel
Elsevier 1997; US$ 240.00Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform... more...
Logarithmic Forms and Diophantine Geometryby A. Baker; G. Wüstholz
Cambridge University Press 2008; US$ 68.00An account of effective methods in transcendental number theory and Diophantine geometry by eminent authors. more...
The Large Sieve and its Applicationsby Emmanuel Kowalski
Cambridge University Press 2008; US$ 85.00Explains new applications of the 'large sieve', an important tool of analytic number theory, presenting potential uses beyond this area. more...
Diophantine Approximationby Robert F. Tichy; Hans Peter Schlickewei; Klaus Schmidt
Springer 2008; US$ 159.00This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation. This includes contributions to Wolfgang Schmidt's subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavour. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and discrepancy theory. The articles are based on lectures given at a conference at... more...
Distribution Theory of Algebraic Numbersby Pei-Chu Hu; Chung-Chun Yang
Walter de Gruyter, Inc. 2008; US$ 165.00The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions ? Algebraic numbers ? Algebraic geometry ? Height functions ? The abc-conjecture ? Roth's theorem ? Subspace theorems ? Vojta's conjectures ? L-functions. more...
Applied Algebraic Dynamicsby Vladimir Anashin; Andrei Khrennikov
Walter de Gruyter, Inc. 2009; US$ 140.00This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis. more...









