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 265 pages. 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.
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.
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.
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.
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.
Download or read book Families of Varieties of General Type written by János Kollár and published by Cambridge University Press. This book was released on 2023-04-30 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Download or read book Fractional Sobolev Spaces and Inequalities written by D. E. Edmunds and published by Cambridge University Press. This book was released on 2022-10-31 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by Cambridge University Press. This book was released on 2022-11-30 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.
Download or read book Modular And Automorphic Forms Beyond written by Hossein Movasati and published by World Scientific. This book was released on 2021-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.
Download or read book The Mordell Conjecture written by Hideaki Ikoma and published by Cambridge University Press. This book was released on 2022-02-03 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Contributions to the Theory of Transcendental Numbers written by Gregory Chudnovsky and published by American Mathematical Soc.. This book was released on 1984 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.
Download or read book Function Field Arithmetic written by Dinesh S. Thakur and published by World Scientific. This book was released on 2004 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an exposition of function field arithmetic withemphasis on recent developments concerning Drinfeld modules, thearithmetic of special values of transcendental functions (such as zetaand gamma functions and their interpolations), diophantineapproximation and related interesting open problems.
Download or read book Noncommutative Geometry Arithmetic and Related Topics written by Caterina Consani and published by JHU Press. This book was released on 2011 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
Download or read book Renormalization and Galois Theories written by Frédéric Fauvet and published by European Mathematical Society. This book was released on 2009 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.
Download or read book Surveys in Number Theory written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).
Download or read book Diophantine Approximation and Transcendence Theory written by Gisbert Wüstholz and published by Springer. This book was released on 2006-11-15 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
