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Author: Annette Huber Publisher: Cambridge University Press ISBN: 1316519937 Category : Mathematics Languages : en Pages : 265
Book Description
Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Author: Annette Huber Publisher: Cambridge University Press ISBN: 1316519937 Category : Mathematics Languages : en Pages : 265
Book Description
Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.
Author: Annette Huber Publisher: Cambridge University Press ISBN: 1009022717 Category : Mathematics Languages : en Pages : 266
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.
Author: Alan Baker Publisher: Cambridge University Press ISBN: 100922994X Category : Computers Languages : en Pages : 185
Book Description
Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.
Author: Jonathan Pila Publisher: Cambridge University Press ISBN: 1009170325 Category : Mathematics Languages : en Pages : 267
Book Description
Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Author: Alejandro D. de Acosta Publisher: ISBN: 1009063359 Category : Mathematics Languages : en Pages : 264
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.
Author: D. E. Edmunds Publisher: Cambridge University Press ISBN: 1009254634 Category : Mathematics Languages : en Pages : 169
Book Description
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Author: Hossein Movasati Publisher: World Scientific ISBN: 9811238693 Category : Mathematics Languages : en Pages : 323
Book Description
The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.
Author: Hideaki Ikoma Publisher: Cambridge University Press ISBN: 1108998194 Category : Mathematics Languages : en Pages : 180
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.
Author: Annette Huber
Author: Annette Huber
Author: Annette Huber
Author: Alan Baker
Author: Jonathan Pila
Author: Alejandro D. de Acosta
Author: János Kollár
Author: D. E. Edmunds
Author: Shmuel Weinberger
Author: Hossein Movasati
Author: Hideaki Ikoma