Transcendence and Linear Relations of 1-Periods

Transcendence and Linear Relations of 1-Periods PDF Author: Annette Huber
Publisher: Cambridge University Press
ISBN: 1009022717
Category : Mathematics
Languages : en
Pages : 266

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Book Description
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.

Transcendence and Linear Relations of 1-Periods

Transcendence and Linear Relations of 1-Periods PDF Author: Annette Huber
Publisher: Cambridge University Press
ISBN: 1009022717
Category : Mathematics
Languages : en
Pages : 266

Get Book Here

Book Description
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.

Transcendence and Linear Relations of 1-Periods

Transcendence and Linear Relations of 1-Periods PDF Author: Annette Huber
Publisher: Cambridge University Press
ISBN: 1316519937
Category : Mathematics
Languages : en
Pages : 265

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Book Description
Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.

Periods And Special Functions In Transcendence

Periods And Special Functions In Transcendence PDF Author: Paula B Tretkoff
Publisher: World Scientific
ISBN: 1786342960
Category : Mathematics
Languages : en
Pages : 229

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Book Description
'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate … The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi-Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Transcendental Number Theory

Transcendental Number Theory PDF Author: Alan Baker
Publisher: Cambridge University Press
ISBN: 100922994X
Category : Computers
Languages : en
Pages : 185

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Book Description
Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Point-Counting and the Zilber–Pink Conjecture

Point-Counting and the Zilber–Pink Conjecture PDF Author: Jonathan Pila
Publisher: Cambridge University Press
ISBN: 1009170325
Category : Mathematics
Languages : en
Pages : 267

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Book Description
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.

Large Deviations for Markov Chains

Large Deviations for Markov Chains PDF Author: Alejandro D. de Acosta
Publisher:
ISBN: 1009063359
Category : Mathematics
Languages : en
Pages : 264

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Book Description
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.

Families of Varieties of General Type

Families of Varieties of General Type PDF Author: János Kollár
Publisher: Cambridge University Press
ISBN: 1009346105
Category : Mathematics
Languages : en
Pages : 491

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Book Description
The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Fractional Sobolev Spaces and Inequalities

Fractional Sobolev Spaces and Inequalities PDF Author: D. E. Edmunds
Publisher: Cambridge University Press
ISBN: 1009254634
Category : Mathematics
Languages : en
Pages : 169

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Book Description
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.

Variations on a Theme of Borel

Variations on a Theme of Borel PDF Author: Shmuel Weinberger
Publisher: Cambridge University Press
ISBN: 1107142598
Category : Mathematics
Languages : en
Pages : 365

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Book Description
Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

The Mordell Conjecture

The Mordell Conjecture PDF Author: Hideaki Ikoma
Publisher: Cambridge University Press
ISBN: 1108998194
Category : Mathematics
Languages : en
Pages : 180

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Book Description
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell–Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.