Mahler Functions And Transcendence
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| Author | : Kumiko Nishioka |
| Publisher | : Springer |
| Total Pages | : 195 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540685987 |
This book is the first comprehensive treatise of the transcendence theory of Mahler functions and their values. Recently the theory has seen profound development and has found a diversity of applications. The book assumes a background in elementary field theory, p-adic field, algebraic function field of one variable and rudiments of ring theory. The book is intended for both graduate students and researchers who are interested in transcendence theory. It will lay the foundations of the theory of Mahler functions and provide a source of further research.
| Author | : Alin Bostan |
| Publisher | : Springer Nature |
| Total Pages | : 544 |
| Release | : 2021-11-02 |
| Genre | : Mathematics |
| ISBN | : 3030843041 |
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
| Author | : Yuri V. Nesterenko |
| Publisher | : Springer |
| Total Pages | : 257 |
| Release | : 2003-07-01 |
| Genre | : Mathematics |
| ISBN | : 3540445501 |
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
| Author | : David Angell |
| Publisher | : CRC Press |
| Total Pages | : 201 |
| Release | : 2021-12-30 |
| Genre | : Mathematics |
| ISBN | : 1000523780 |
Irrationality and Transcendence in Number Theory tells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material. Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation. Suitable as a primary textbook for advanced undergraduate courses in number theory, or as supplementary reading for interested postgraduates. Each chapter concludes with an appendix setting out the basic facts needed from each topic, so that the book is accessible to readers without any specific specialist background.
| Author | : Jürgen Sander |
| Publisher | : Springer |
| Total Pages | : 552 |
| Release | : 2016-12-29 |
| Genre | : Mathematics |
| ISBN | : 3319282034 |
This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.
| Author | : Katsumi Nomizu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 108 |
| Release | : 1996 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9780821804452 |
This book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry.
| Author | : Dennis A. Hejhal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 693 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215447 |
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
| Author | : Dinesh S. Thakur |
| Publisher | : World Scientific |
| Total Pages | : 405 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9812388397 |
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
| Author | : Alan Baker |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2022-06-09 |
| Genre | : Mathematics |
| ISBN | : 1009229966 |
First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.
| Author | : Jonathan M. Borwein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 395 |
| Release | : 2013-05-16 |
| Genre | : Mathematics |
| ISBN | : 1461466423 |
“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.
