The Heat Kernel And Theta Inversion On Sl2 C

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The Heat Kernel and Theta Inversion on SL2(C)

Jay Jorgenson,Serge Lang
The Heat Kernel and Theta Inversion on SL2 C Book PDF

Author : Jay Jorgenson,Serge Lang
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 50,7 Mb
Release : 2009-02-20
Category : Mathematics
ISBN : 9780387380322

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The Heat Kernel and Theta Inversion on SL2(C) by Jay Jorgenson,Serge Lang Pdf

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./

Number Theory, Analysis and Geometry

Dorian Goldfeld,Jay Jorgenson,Peter Jones,Dinakar Ramakrishnan,Kenneth Ribet,John Tate
Number Theory Analysis and Geometry Book PDF

Author : Dorian Goldfeld,Jay Jorgenson,Peter Jones,Dinakar Ramakrishnan,Kenneth Ribet,John Tate
Publisher : Springer Science & Business Media
Page : 715 pages
File Size : 54,6 Mb
Release : 2011-12-21
Category : Mathematics
ISBN : 9781461412601

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Number Theory, Analysis and Geometry by Dorian Goldfeld,Jay Jorgenson,Peter Jones,Dinakar Ramakrishnan,Kenneth Ribet,John Tate Pdf

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.

Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Pascal Auscher,T. Coulhon,Alexander Grigoryan
Heat Kernels and Analysis on Manifolds Graphs and Metric Spaces Book PDF

Author : Pascal Auscher,T. Coulhon,Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 42,7 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821833834

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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by Pascal Auscher,T. Coulhon,Alexander Grigoryan Pdf

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Heat Eisenstein Series on $\mathrm {SL}_n(C)$

Jay Jorgenson,Serge Lang
Heat Eisenstein Series on mathrm SL n C Book PDF

Author : Jay Jorgenson,Serge Lang
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 49,6 Mb
Release : 2009
Category : Decomposition
ISBN : 9780821840443

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Heat Eisenstein Series on $\mathrm {SL}_n(C)$ by Jay Jorgenson,Serge Lang Pdf

The purpose of this Memoir is to define and study multi-variable Eisenstein series attached to heat kernels. Fundamental properties of heat Eisenstein series are proved, and conjectural behavior, including their role in spectral expansions, are stated.

Collected Papers V

Serge Lang
Collected Papers V Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 42,9 Mb
Release : 2000-10-23
Category : Mathematics
ISBN : 0387950303

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Collected Papers V by Serge Lang Pdf

Serge Lang (1927-2005) was one of the top mathematicians of our time. He was born in Paris in 1927, and moved with his family to California, where he graduated from Beverly Hills High School in 1943. He subsequently graduated from California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951 before holding faculty positions at the University of Chicago and Columbia University (1955-1971). At the time of his death he was professor emeritus of Mathematics at Yale University. An excellent writer, Lang has made innumerable and invaluable contributions in diverse fields of mathematics. He was perhaps best known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was also a member of the Bourbaki group. He was honored with the Cole Prize by the American Mathematical Society as well as with the Prix Carrière by the French Academy of Sciences. These five volumes collect the majority of his research papers, which range over a variety of topics.

The Ubiquitous Heat Kernel

Jay Jorgenson,American Mathematical Society
The Ubiquitous Heat Kernel Book PDF

Author : Jay Jorgenson,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 52,9 Mb
Release : 2006
Category : Geometry, Algebraic
ISBN : 9780821836989

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The Ubiquitous Heat Kernel by Jay Jorgenson,American Mathematical Society Pdf

The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

Complex Analysis

Elias M. Stein,Rami Shakarchi
Complex Analysis Book PDF

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 398 pages
File Size : 41,9 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781400831159

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Complex Analysis by Elias M. Stein,Rami Shakarchi Pdf

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Gauge/Gravity Duality

Martin Ammon,Johanna Erdmenger
Gauge Gravity Duality Book PDF

Author : Martin Ammon,Johanna Erdmenger
Publisher : Cambridge University Press
Page : 549 pages
File Size : 45,9 Mb
Release : 2015-04-09
Category : Science
ISBN : 9781107010345

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Gauge/Gravity Duality by Martin Ammon,Johanna Erdmenger Pdf

The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Dirichlet Branes and Mirror Symmetry

Paul Aspinwall
Dirichlet Branes and Mirror Symmetry Book PDF

Author : Paul Aspinwall
Publisher : American Mathematical Soc.
Page : 698 pages
File Size : 48,8 Mb
Release : 2009
Category : D-branes
ISBN : 9780821838488

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Dirichlet Branes and Mirror Symmetry by Paul Aspinwall Pdf

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Complex Analysis

Serge Lang
Complex Analysis Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 44,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475718713

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Complex Analysis by Serge Lang Pdf

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Quantum Theory, Groups and Representations

Peter Woit
Quantum Theory Groups and Representations Book PDF

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 55,7 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

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Quantum Theory, Groups and Representations by Peter Woit Pdf

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Math Talks for Undergraduates

Serge Lang
Math Talks for Undergraduates Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461214762

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Math Talks for Undergraduates by Serge Lang Pdf

For many years, Serge Lang has given talks on selected items in mathematics which could be extracted at a level understandable by those who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book covering such topics as: prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, and harmonic and symmetric polynomials. Each talk is written in a lively and informal style meant to engage any reader looking for further insight into mathematics.

The Beauty of Doing Mathematics

Serge Lang
The Beauty of Doing Mathematics Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 40,5 Mb
Release : 1985-09-04
Category : Mathematics
ISBN : 0387961496

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The Beauty of Doing Mathematics by Serge Lang Pdf

If someone told you that mathematics is quite beautiful, you might be surprised. But you should know that some people do mathematics all their lives, and create mathematics, just as a composer creates music. Usually, every time a mathematician solves a problem, this gives rise to many oth ers, new and just as beautiful as the one which was solved. Of course, often these problems are quite difficult, and as in other disciplines can be understood only by those who have studied the subject with some depth, and know the subject well. In 1981, Jean Brette, who is responsible for the Mathematics Section of the Palais de la Decouverte (Science Museum) in Paris, invited me to give a conference at the Palais. I had never given such a conference before, to a non-mathematical public. Here was a challenge: could I communicate to such a Saturday afternoon audience what it means to do mathematics, and why one does mathematics? By "mathematics" I mean pure mathematics. This doesn't mean that pure math is better than other types of math, but I and a number of others do pure mathematics, and it's about them that I am now concerned. Math has a bad reputation, stemming from the most elementary levels. The word is in fact used in many different contexts. First, I had to explain briefly these possible contexts, and the one with which I wanted to deal.

String Theory in a Nutshell

Elias Kiritsis
String Theory in a Nutshell Book PDF

Author : Elias Kiritsis
Publisher : Princeton University Press
Page : 888 pages
File Size : 42,6 Mb
Release : 2019-04-16
Category : Science
ISBN : 9780691188966

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String Theory in a Nutshell by Elias Kiritsis Pdf

The essential introduction to modern string theory—now fully expanded and revised String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world’s leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature. This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly. The essential one-volume reference for students and researchers in theoretical high-energy physics Now fully expanded and revised Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems An online illustration package is available to professors

Representations of Linear Groups

Rolf Berndt
Representations of Linear Groups Book PDF

Author : Rolf Berndt
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 43,6 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9783834894014

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Representations of Linear Groups by Rolf Berndt Pdf

This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view.