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Transcendence and Linear Relations of 1-Periods

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Release : 2022-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 937/5 ( reviews)

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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. This book was released on 2022-05-26. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.

Transcendence and Linear Relations of 1-Periods

Download Transcendence and Linear Relations of 1-Periods PDF Online Free

Author :
Release : 2022-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 717/5 ( reviews)

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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. This book was released on 2022-05-26. 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.

Transcendental Number Theory

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Release : 2022-06-09
Genre : Computers
Kind : eBook
Book Rating : 94X/5 ( reviews)

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Book Synopsis Transcendental Number Theory by : Alan Baker

Download or read book Transcendental Number Theory written by Alan Baker. This book was released on 2022-06-09. 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.

Point-Counting and the Zilber–Pink Conjecture

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Release : 2022-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 325/5 ( reviews)

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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. This book was released on 2022-06-09. 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.

Large Deviations for Markov Chains

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Release : 2022-10-12
Genre : Mathematics
Kind : eBook
Book Rating : 359/5 ( reviews)

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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. This book was released on 2022-10-12. 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.

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