Author: Hans Günther Kopetzky
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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Book Description

Author: Hervé Queffélec
Publisher: Springer Nature
ISBN: 9811593515
Category : Mathematics
Languages : en
Pages : 300

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Book Description
The second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition operators, and connections between these two domains which often occur through the Kronecker approximation theorem and the Bohr lift. The book initially discusses Harmonic analysis, including a sharp form of the uncertainty principle, Ergodic theory and Diophantine approximation, basics on continued fractions expansions, and the mixing property of the Gauss map and goes on to present the general theory of Dirichlet series with classes of examples connected to continued fractions, Bohr lift, sharp forms of the Bohnenblust–Hille theorem, Hardy–Dirichlet spaces, composition operators of the Hardy–Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory, and ergodic theory, featuring the richness of analytic theory of Dirichlet series. This self-contained book benefits beginners as well as researchers.

Author: Michel Waldschmidt
Publisher: Springer Science & Business Media
ISBN: 3662115697
Category : Mathematics
Languages : en
Pages : 649

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Book Description
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

Author: Ivan Niven
Publisher: Courier Corporation
ISBN: 0486164705
Category : Mathematics
Languages : en
Pages : 82

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Book Description
This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of complex numbers, and product of complex linear forms. 1963 edition.

Author: Wolfgang M. Schmidt
Publisher: Springer Science & Business Media
ISBN: 3540403922
Category : Diophantine analysis
Languages : en
Pages : 359

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Book Description

Author: Edward B. Burger
Publisher: American Mathematical Soc.
ISBN: 0821826409
Category : Mathematics
Languages : en
Pages : 160

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Book Description
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.

Author: Wolfgang M. Schmidt
Publisher: Springer
ISBN: 3540473742
Category : Mathematics
Languages : en
Pages : 224

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Book Description
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum

Author: Robert F. Tichy
Publisher: Springer Science & Business Media
ISBN: 3211742808
Category : Mathematics
Languages : en
Pages : 416

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Book Description
This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrödinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.

Author: Umberto Zannier
Publisher: Springer
ISBN: 8876425179
Category : Mathematics
Languages : en
Pages : 248

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Book Description
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.

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097606
Category : Mathematics
Languages : en
Pages : 381

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Book Description
A comprehensive, graduate-level treatment of unit equations and their various applications.