Diophantine Approximation and Dirichlet Series PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Diophantine Approximation and Dirichlet Series PDF full book. Access full book title Diophantine Approximation and Dirichlet Series by Hervé Queffélec. Download full books in PDF and EPUB format.
Author: Hervé Queffélec
Publisher: Springer Nature
ISBN: 9811593515
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
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: Hervé Queffélec
Publisher: Springer Nature
ISBN: 9811593515
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
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: Godfrey Harold Hardy
Publisher:
ISBN:
Category : Diophantine analysis
Languages : en
Pages : 17
Get Book Here
Book Description
Author: Wolfgang M. Schmidt
Publisher: Springer Science & Business Media
ISBN: 3540403922
Category : Diophantine analysis
Languages : en
Pages : 359
Get Book Here
Book Description
Author: Source Wikipedia
Publisher: University-Press.org
ISBN: 9781230565538
Category :
Languages : en
Pages : 62
Get Book Here
Book Description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 26. Chapters: Auxiliary function, Beatty sequence, Constructions of low-discrepancy sequences, Davenport-Schmidt theorem, Dirichlet's approximation theorem, Discrepancy of hypergraphs, Discrepancy theory, Duffin-Schaeffer conjecture, Equidistributed sequence, Equidistribution theorem, Harmonious set, Hurwitz's theorem (number theory), Kronecker's theorem, Lagrange number, Liouville number, Littlewood conjecture, Markov number, Markov spectrum, Oppenheim conjecture, Proof that e is irrational, Restricted partial quotients, Schneider-Lang theorem, Siegel's lemma, Subspace theorem, Thue-Siegel-Roth theorem, Van der Corput sequence, Weyl's criterion, Weyl's inequality.
Author: Ivan Niven
Publisher: Courier Corporation
ISBN: 0486164705
Category : Mathematics
Languages : en
Pages : 82
Get Book Here
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: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 9780387944562
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere. Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.
Author: Robert F. Tichy
Publisher: Springer Science & Business Media
ISBN: 3211742808
Category : Mathematics
Languages : en
Pages : 416
Get Book Here
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: Michel Waldschmidt
Publisher: Springer Science & Business Media
ISBN: 3662115697
Category : Mathematics
Languages : en
Pages : 649
Get Book Here
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: Andreas Defant
Publisher: Cambridge University Press
ISBN: 1108476716
Category : Mathematics
Languages : en
Pages : 709
Get Book Here
Book Description
Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Author: Hans Günther Kopetzky
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Get Book Here
Book Description
