Number Theory Trace Formulas And Discrete Groups
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Number Theory Trace Formulas And Discrete Groups
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Author : Atle Selberg
language : en
Publisher:
Release Date : 1989
Number Theory Trace Formulas And Discrete Groups written by Atle Selberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with MATHEMATICS categories.
Number Theory, Trace Formulas and Discrete Groups.
Arithmetic Groups And Their Generalizations
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Arithmetic Groups And Their Generalizations written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Number Theory And Modular Forms
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Author : Bruce C. Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Number Theory And Modular Forms written by Bruce C. Berndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.
Dynamics Geometry Number Theory
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Author : David Fisher
language : en
Publisher: University of Chicago Press
Release Date : 2022-02-07
Dynamics Geometry Number Theory written by David Fisher and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-07 with Mathematics categories.
This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.
Sieves In Number Theory
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Author : George Greaves
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Sieves In Number Theory written by George Greaves and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Slightly more than 25 years ago, the first text devoted entirely to sieve meth ods made its appearance, rapidly to become a standard source and reference in the subject. The book of H. Halberstam and H.-E. Richert had actually been conceived in the mid-1960's. The initial stimulus had been provided by the paper of W. B. Jurkat and Richert, which determined the sifting limit for the linear sieve, using a combination of the ,A2 method of A. Selberg with combinatorial ideas which were in themselves of great importance and in terest. One of the declared objectives in writing their book was to place on record the sharpest form of what they called Selberg sieve theory available at the time. At the same time combinatorial methods were not neglected, and Halber stam and Richert included an account of the purely combinatorial method of Brun, which they believed to be worthy of further examination. Necessar ily they included only a briefer mention of the development of these ideas due (independently) to J. B. Rosser and H. Iwaniec that became generally available around 1971. These combinatorial notions have played a central part in subsequent developments, most notably in the papers of Iwaniec, and a further account may be thought to be timely. There have also been some developments in the theory of the so-called sieve with weights, and an account of these will also be included in this book.
Recent Perspectives In Random Matrix Theory And Number Theory
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Author : F. Mezzadri
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-21
Recent Perspectives In Random Matrix Theory And Number Theory written by F. Mezzadri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.
Provides a grounding in random matrix techniques applied to analytic number theory.
Basic Structures Of Function Field Arithmetic
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Author : David Goss
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Basic Structures Of Function Field Arithmetic written by David Goss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
The Goldbach Conjecture
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Author : Yuan Wang
language : en
Publisher: World Scientific
Release Date : 2002
The Goldbach Conjecture written by Yuan Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book provides a detailed description of a most important unsolved mathematical problem OCo the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920''s. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture."
Multiplicative Number Theory I
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Author : Hugh L. Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2007
Multiplicative Number Theory I written by Hugh L. Montgomery and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Handbook Of Number Theory I
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Author : József Sándor
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-17
Handbook Of Number Theory I written by József Sándor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-17 with Mathematics categories.
This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.