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The Zeta Factor
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Book Synopsis Zeta Functions Of Reductive Groups And Their Zeros by : Lin Weng
Download or read book Zeta Functions Of Reductive Groups And Their Zeros written by Lin Weng and published by World Scientific. This book was released on 2018-02-09 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields. Namely, the geometric one, built up from stability of principal lattices and an arithmetic cohomology theory, and the analytic one, from Langlands' theory of Eisenstein systems and some techniques used in trace formula, respectively. Apparently different, they are unified via a Lafforgue type relation between Arthur's analytic truncations and parabolic reductions of Harder-Narasimhan and Atiyah-Bott. Dominated by the stability condition and/or the Lie structures embedded in, these zeta functions have a standard form of the functional equation, admit much more refined symmetric structures, and most surprisingly, satisfy a weak Riemann hypothesis. In addition, two levels of the distributions for their zeros are exposed, i.e. a classical one giving the Dirac symbol, and a secondary one conjecturally related to GUE.This book is written not only for experts, but for graduate students as well. For example, it offers a summary of basic theories on Eisenstein series and stability of lattices and arithmetic principal torsors. The second part on rank two zeta functions can be used as an introduction course, containing a Siegel type treatment of cusps and fundamental domains, and an elementary approach to the trace formula involved. Being in the junctions of several branches and advanced topics of mathematics, these works are very complicated, the results are fundamental, and the theory exposes a fertile area for further research.
Book Synopsis An Approach to the Selberg Trace Formula via the Selberg Zeta-Function by : Jürgen Fischer
Download or read book An Approach to the Selberg Trace Formula via the Selberg Zeta-Function written by Jürgen Fischer and published by Springer. This book was released on 2006-11-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-function. Apart from the basic spectral theory of the Laplacian for cofinite groups the book is self-contained and will be useful as a quick approach to the Selberg zeta-function and the Selberg trace formula.
Book Synopsis The Theory of Zeta-Functions of Root Systems by : Yasushi Komori
Download or read book The Theory of Zeta-Functions of Root Systems written by Yasushi Komori and published by Springer Nature. This book was released on 2024-02-03 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.
Download or read book Purple, Green and Gold written by and published by . This book was released on 1924 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Character Traits as Factors in Intelligence Test Performance by : William Moseley Brown
Download or read book Character Traits as Factors in Intelligence Test Performance written by William Moseley Brown and published by . This book was released on 1923 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Treatise on Geophysics written by and published by Elsevier. This book was released on 2015-04-17 with total page 5604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treatise on Geophysics, Second Edition, is a comprehensive and in-depth study of the physics of the Earth beyond what any geophysics text has provided previously. Thoroughly revised and updated, it provides fundamental and state-of-the-art discussion of all aspects of geophysics. A highlight of the second edition is a new volume on Near Surface Geophysics that discusses the role of geophysics in the exploitation and conservation of natural resources and the assessment of degradation of natural systems by pollution. Additional features include new material in the Planets and Moon, Mantle Dynamics, Core Dynamics, Crustal and Lithosphere Dynamics, Evolution of the Earth, and Geodesy volumes. New material is also presented on the uses of Earth gravity measurements. This title is essential for professionals, researchers, professors, and advanced undergraduate and graduate students in the fields of Geophysics and Earth system science. Comprehensive and detailed coverage of all aspects of geophysics Fundamental and state-of-the-art discussions of all research topics Integration of topics into a coherent whole
Book Synopsis Pseudodifferential Operators with Automorphic Symbols by : André Unterberger
Download or read book Pseudodifferential Operators with Automorphic Symbols written by André Unterberger and published by Birkhäuser. This book was released on 2015-06-22 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Book Synopsis Elliptic Curves by : Dale Husemöller
Download or read book Elliptic Curves written by Dale Husemöller and published by Springer Science & Business Media. This book was released on 2006-06-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices
Book Synopsis Essential Immunology for Surgeons by : Oleg Eremin
Download or read book Essential Immunology for Surgeons written by Oleg Eremin and published by Oxford University Press, USA. This book was released on 2011-04-28 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the necessary foundation for a critical understanding of this rapidly expanding area of biological science that underpins and explains the modern concepts of a wide range of diseases and conditions, this book gives a concise, readable, and up-to-date account of immunology in general and its translation into key areas of clinical practice.
Book Synopsis Airborne Wind Energy by : Uwe Ahrens
Download or read book Airborne Wind Energy written by Uwe Ahrens and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference offers an overview of the field of airborne wind energy. As the first book of its kind, it provides a consistent compilation of the fundamental theories, a compendium of current research and development activities as well as economic and regulatory aspects. In five parts, the book demonstrates the relevance of Airborne Wind Energy and the role that this emerging field of technology can play for the transition towards a renewable energy economy. Part I on "Fundamentals" contains seven general chapters explaining the principles of airborne wind energy and its different variants, of meteorology, the history of kites and financing strategies. Part II on "System Modeling, Optimization and Control" contains eight contributions that develop and use detailed dynamic models for simulation, optimization, and control of airborne wind energy systems, while Part III on "Analysis of Flexible Kite Dynamics" collects four chapters that focus on the particularly challenging simulation problems related to flexible kites. Part IV "Implemented Concepts" contains eleven contributions each of which presents developed prototypes together with real-world experimental results obtained with the different concepts. Finally, in Part V on "Component Design", five papers are collected that address in detail the technical challenges for some of the components of airborne wind energy. Airborne Wind Energy presents all basics in a single source to someone starting to explore wind power in the upper atmosphere and serves as a valuable reference for researchers, scientists, professionals and students active in the innovative field of Airborne Wind Energy.
Book Synopsis Transmission Electron Microscopy by : David B. Williams
Download or read book Transmission Electron Microscopy written by David B. Williams and published by Springer Science & Business Media. This book was released on 2009-08-05 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking text has been established as the market leader throughout the world. Profusely illustrated, the book provides the necessary instructions for successful hands-on application of this versatile materials characterization technique.
Book Synopsis Quantization and Arithmetic by : André Unterberger
Download or read book Quantization and Arithmetic written by André Unterberger and published by Springer Science & Business Media. This book was released on 2008-09-28 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: (12) (4) Let ? be the unique even non-trivial Dirichlet character mod 12, and let ? be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions m (12) ? d (x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2 m?Z 2 i?x UnderaFouriertransformation,orundermultiplicationbythefunctionx ? e , the?rst(resp. second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th (resp. 8th) root of unity. Then, consider the metaplectic representation Met, 2 a unitary representation in L (R) of the metaplectic group G, the twofold cover of the group G = SL(2,R), the de?nition of which will be recalled in Section 2: it extends as a representation in the spaceS (R) of tempered distributions. From what has just been said, if g ̃ is a point of G lying above g? G,andif d = d even g ̃ ?1 or d , the distribution d =Met(g ̃ )d only depends on the class of g in the odd homogeneousspace?\G=SL(2,Z)\G,uptomultiplicationbysomephasefactor, by which we mean any complex number of absolute value 1 depending only on g ̃. On the other hand, a function u?S(R) is perfectly characterized by its scalar g ̃ productsagainstthedistributionsd ,sinceonehasforsomeappropriateconstants C , C the identities 0 1 g ̃ 2 2 | d ,u | dg = C u if u is even, 2 0 even L (R) ?\G
Book Synopsis Biomarkers for Heart Failure, An Issue of Heart Failure Clinics by : Toru Suzuki
Download or read book Biomarkers for Heart Failure, An Issue of Heart Failure Clinics written by Toru Suzuki and published by Elsevier Health Sciences. This book was released on 2017-11-27 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This issue of Heart Failure Clinics, edited by Dr. Toru Suzuki, will cover Biomarkers for Heart Failure, including but not limited to Proenkephalin, B-type and mid-regional pro atrial natriuretic peptides , N-terminal B-type natriuretic peptide, Soluble T2, Adrenomedullin, Copeptin, Non-Coding RNAs, Troponin, Growth differentiation factor (GDF-15) , Galectin-3, Proteomic biomarkers, and Metabolic biomarkers .
Book Synopsis Mathematical Foundations of Computer Science 2014 by : Ersébet Csuhaj-Varjú
Download or read book Mathematical Foundations of Computer Science 2014 written by Ersébet Csuhaj-Varjú and published by Springer. This book was released on 2014-08-12 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.
Download or read book Collected Papers V written by Serge Lang and published by Springer Science & Business Media. This book was released on 2000-10-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Explicit Formulas by : Jay Jorgenson
Download or read book Explicit Formulas written by Jay Jorgenson and published by Springer. This book was released on 2006-11-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.
Book Synopsis Advances in Atomic Spectroscopy by : J. Sneddon
Download or read book Advances in Atomic Spectroscopy written by J. Sneddon and published by Elsevier. This book was released on 1995-06-14 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series describes selected advances in the area of atomic spectroscopy. It is promarily intended for the reader who has a background in atmoic spectroscopy; suitable to the novice and expert. Although a widely used and accepted method for metal and non-metal analysis in a variety of complex samples, Advances in Atomic Spectroscopy covers a wide range of materials. Each Chapter will completely cover an area of atomic spectroscopy where rapid development has occurred.
