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Author | : Gorō Shimura |
Publisher | : Princeton University Press |
Total Pages | : 292 |
Release | : 1971-08-21 |
Genre | : Mathematics |
ISBN | : 9780691080925 |
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Author | : Burt Totaro |
Publisher | : Cambridge University Press |
Total Pages | : 245 |
Release | : 2014-06-26 |
Genre | : Mathematics |
ISBN | : 113991605X |
Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.
Author | : R.J. Zimmer |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1468494880 |
This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidity, arithmeticity, and structure of lattices in semi simple groups, and related work of the author on the actions of semisimple groups and their lattice subgroups. In doing so, we develop the necessary prerequisites from earlier work of Borel, Furstenberg, Kazhdan, Moore, and others. One of the difficulties involved in an exposition of this material is the continuous interplay between ideas from the theory of algebraic groups on the one hand and ergodic theory on the other. This, of course, is not so much a mathematical difficulty as a cultural one, as the number of persons comfortable in both areas has not traditionally been large. We hope this work will also serve as a contribution towards improving that situation. While there are a number of satisfactory introductory expositions of the ergodic theory of integer or real line actions, there is no such exposition of the type of ergodic theoretic results with which we shall be dealing (concerning actions of more general groups), and hence we have assumed absolutely no knowledge of ergodic theory (not even the definition of "ergodic") on the part of the reader. All results are developed in full detail.
Author | : Oliver Heaviside |
Publisher | : |
Total Pages | : 578 |
Release | : 1922 |
Genre | : Electric waves |
ISBN | : |
Author | : Rockefeller University |
Publisher | : |
Total Pages | : 934 |
Release | : 1913 |
Genre | : Medicine |
ISBN | : |
Author | : Wenbin Guo |
Publisher | : Springer |
Total Pages | : 369 |
Release | : 2015-04-23 |
Genre | : Mathematics |
ISBN | : 3662457474 |
This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.
Author | : Rockefeller Institute for Medical Research |
Publisher | : |
Total Pages | : 696 |
Release | : 1913 |
Genre | : Medicine |
ISBN | : |
Author | : Arthur Messinger Comey |
Publisher | : |
Total Pages | : 1186 |
Release | : 1921 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 252 |
Release | : 1923 |
Genre | : |
ISBN | : |
Author | : Johannes Blümlein |
Publisher | : Springer |
Total Pages | : 509 |
Release | : 2019-01-30 |
Genre | : Computers |
ISBN | : 3030044807 |
This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.