On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp 4 The Fundamental Lemma
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On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp 4 The Fundamental Lemma
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Author : Masaaki Furusawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp 4 The Fundamental Lemma written by Masaaki Furusawa 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 2003 with Mathematics categories.
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
On Central Critical Values Of The Degree Four L Functions For Gsp 4
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Author : Masaaki Furusawa
language : en
Publisher:
Release Date : 2014-09-11
On Central Critical Values Of The Degree Four L Functions For Gsp 4 written by Masaaki Furusawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Automorphic forms categories.
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of B{uml}ocherer's conjecture on the central critical values of the degree four L-functions for GSp(4), and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.
On Central Critical Values Of The Degree Four L Functions For Gsp 4
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Author : Masaaki Furusawa
language : en
Publisher:
Release Date : 2014-09-11
On Central Critical Values Of The Degree Four L Functions For Gsp 4 written by Masaaki Furusawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Automorphic forms categories.
Statement of results Gauss sum, Kloosterman sum and Salie sum Matrix argument Kloosterman sums Evaluation of the Novodvorsky orbital integral Evaluation of the Bessel orbital integral Evaluation of the quadratic orbital integral Bibliography.
The Theory Of Jacobi Forms
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Author : Martin Eichler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
The Theory Of Jacobi Forms written by Martin Eichler 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 2013-12-14 with Mathematics categories.
The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.
Introductory Lectures On Siegel Modular Forms
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Author : Helmut Klingen
language : en
Publisher: Cambridge University Press
Release Date : 1990-02-23
Introductory Lectures On Siegel Modular Forms written by Helmut Klingen 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 1990-02-23 with Mathematics categories.
From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.
The Abel Prize 2013 2017
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Author : Helge Holden
language : en
Publisher: Springer
Release Date : 2019-02-23
The Abel Prize 2013 2017 written by Helge Holden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-23 with Mathematics categories.
The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.
Control And System Theory Of Discrete Time Stochastic Systems
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Author : Jan H. van Schuppen
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Control And System Theory Of Discrete Time Stochastic Systems written by Jan H. van Schuppen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Technology & Engineering categories.
This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.
Imaging Biomarkers
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Author : Luis Martí-Bonmatí
language : en
Publisher: Springer
Release Date : 2016-11-03
Imaging Biomarkers written by Luis Martí-Bonmatí and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-03 with Medical categories.
This is the first book to cover all aspects of the development of imaging biomarkers and their integration into clinical practice, from the conceptual basis through to the technical aspects that need to be considered in order to ensure that medical imaging can serve as a powerful quantification instrument capable of providing valuable information on organ and tissue properties. The process of imaging biomarker development is considered step by step, covering proof of concept, proof of mechanism, image acquisition, image preparation, imaging biomarker analysis and measurement, detection of measurement biases (proof of principle), proof of efficacy and effectiveness, and reporting of results. Sources of uncertainty in the accuracy and precision of measurements and pearls and pitfalls in gold standards and biological correlation are discussed. In addition, practical use cases are included on imaging biomarker implementation in brain, oncologic, cardiovascular, musculoskeletal, and abdominal diseases. The authors are a multidisciplinary team of expert radiologists and engineers, and the book will be of value to all with an interest in the quantitative imaging of biomarkers in personalized medicine.
Representations Of The Infinite Symmetric Group
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Author : Alexei Borodin
language : en
Publisher: Cambridge University Press
Release Date : 2017
Representations Of The Infinite Symmetric Group written by Alexei Borodin 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 2017 with Mathematics categories.
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Algebraic Geometry
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Author : Ulrich Görtz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-06
Algebraic Geometry written by Ulrich Görtz 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 2010-08-06 with Mathematics categories.
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.