Applications of Diophantine Approximation to Integral Points and Transcendence

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Publisher : Cambridge University Press
ISBN 13 : 1108424945
Total Pages : 209 pages
Book Rating : 4.43/5 ( download)

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Book Synopsis Applications of Diophantine Approximation to Integral Points and Transcendence by : Pietro Corvaja

Download or read book Applications of Diophantine Approximation to Integral Points and Transcendence written by Pietro Corvaja and published by Cambridge University Press. This book was released on 2018-05-03 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Diophantine approximation and equations focusing on Schmidt's subspace theorem, with applications to transcendence.

On Some Applications of Diophantine Approximations

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Publisher : Springer
ISBN 13 : 8876425209
Total Pages : 169 pages
Book Rating : 4.02/5 ( download)

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Book Synopsis On Some Applications of Diophantine Approximations by : Umberto Zannier

Download or read book On Some Applications of Diophantine Approximations written by Umberto Zannier and published by Springer. This book was released on 2015-02-13 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

Transcendence and Linear Relations of 1-Periods

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Publisher : Cambridge University Press
ISBN 13 : 1009022717
Total Pages : 266 pages
Book Rating : 4.12/5 ( download)

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Book Synopsis Transcendence and Linear Relations of 1-Periods by : Annette Huber

Download or read book Transcendence and Linear Relations of 1-Periods written by Annette Huber and published by Cambridge University Press. This book was released on 2022-05-26 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.

New Advances in Transcendence Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521335454
Total Pages : 456 pages
Book Rating : 4.50/5 ( download)

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Book Synopsis New Advances in Transcendence Theory by : Alan Baker

Download or read book New Advances in Transcendence Theory written by Alan Baker and published by Cambridge University Press. This book was released on 1988-10-13 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.

Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces

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Publisher : Springer Nature
ISBN 13 : 3030498646
Total Pages : 247 pages
Book Rating : 4.41/5 ( download)

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Book Synopsis Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces by : Marc-Hubert Nicole

Download or read book Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces written by Marc-Hubert Nicole and published by Springer Nature. This book was released on 2020-10-31 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective; A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case; An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties. Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.

Point-Counting and the Zilber–Pink Conjecture

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Publisher : Cambridge University Press
ISBN 13 : 1009170325
Total Pages : 267 pages
Book Rating : 4.21/5 ( download)

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Book Synopsis Point-Counting and the Zilber–Pink Conjecture by : Jonathan Pila

Download or read book Point-Counting and the Zilber–Pink Conjecture written by Jonathan Pila and published by Cambridge University Press. This book was released on 2022-06-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.

Transcendental Number Theory

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Publisher : Cambridge University Press
ISBN 13 : 100922994X
Total Pages : 185 pages
Book Rating : 4.44/5 ( download)

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Book Synopsis Transcendental Number Theory by : Alan Baker

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Noncommutative Function-Theoretic Operator Theory and Applications

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Publisher : Cambridge University Press
ISBN 13 : 131651899X
Total Pages : 439 pages
Book Rating : 4.91/5 ( download)

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Book Synopsis Noncommutative Function-Theoretic Operator Theory and Applications by : Joseph A. Ball

Download or read book Noncommutative Function-Theoretic Operator Theory and Applications written by Joseph A. Ball and published by Cambridge University Press. This book was released on 2021-12-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.

Diophantine Approximation and Its Applications

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Publisher :
ISBN 13 :
Total Pages : 355 pages
Book Rating : 4.43/5 ( download)

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Book Synopsis Diophantine Approximation and Its Applications by : Charles F. Osgood

Download or read book Diophantine Approximation and Its Applications written by Charles F. Osgood and published by . This book was released on 1973 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large Deviations for Markov Chains

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Publisher :
ISBN 13 : 1009063359
Total Pages : 264 pages
Book Rating : 4.57/5 ( download)

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Book Synopsis Large Deviations for Markov Chains by : Alejandro D. de Acosta

Download or read book Large Deviations for Markov Chains written by Alejandro D. de Acosta and published by . This book was released on 2022-10-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.