Download or read book On Central Critical Values of the Degree Four L functions for mathrm GSp 4 The Fundamental Lemma written by Masaaki Furusawa and published by American Mathematical Soc.. This book was released on 2003 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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}].
Download or read book On Central Critical Values of the Degree Four L Functions for Gsp 4 written by Masaaki Furusawa and published by . This book was released on 2014-09-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Moments of Automorphic L Functions written by Ming-Ho Ng and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Moments of Automorphic L-functions" by Ming-ho, Ng, 吳銘豪, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: This thesis is devoted to investigation of moments of automorphic L-functions, especially on the central values or the edges of the critical strip of automorphic L-functions. There are nine chapters. Chapter 1 is an introduction and provides some background on the analytic theory of automorphic forms. Chapters 2, 3, 4, 5 and 6 are about L-functions associated to the holomorphic cusp forms, while Chapters 7, 8 and 9 are focused on the L-functions associated to the Maass forms. Chapter 2 is the study of the first moment of the symmetric-square L-functions associated to the holomorphic cusp forms. Asymptotic formulae for the twisted first moment of central values of the symmetric-square L-functions with harmonic weight, in the weight aspect are obtained. The result (in Theorem 2.1.1) extends and improves the known results in the literature. As an application, it is applied to derive an asymptotic formula for the first moment of central values of the symmetric-square L-functions without harmonic weight, under the assumption of the non-negativity of symmetric-square L-functions at the center of critical strip. Analogous new formulae without harmonic weight of the first and second moments of the Hecke L-functions are proved in Chapter 3. Unlike the case in Chapter 2, the results in Chapter 3 are unconditional. In Chapter 4, complex moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the central values of the symmetric square L-functions, with or without harmonic weight, are investigated in the weight aspect. The similar problem in the level aspect was treated by Lau, Royer and Wu. The theme of Chapter 5, as well as Chapter 4, is to examine, in the weight aspect, complex moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the central values of the square L-functions or the square of L-functions, with or without harmonic weight. All the above mentioned results, appeared in Chapters 4 and 5, are in the asymptotic form, that is, given by a formula consisting of a main term and an error term. Chapter 6 investigates the asymptotic behavior of the main terms of the results in Chapters 4 and 5. In particular, precise expansions of high moments are given. In Chapters 7, 8 and 9, the previous studies are carried over to Maass forms in the spectral aspect. The first two moments of central values of symmetric square L-functions associated to Maass forms are computed in Chapter 7. The first four moments of central values of L-functions associated to Maass forms are obtained in Chapter 8. Chapter 9 is to research the mixed moments of central values of symmetric square L-functions twisted by the central values of L-functions or the square of L-functions. These investigations for Maass form are not yet done in the literature. Subjects: L-functions Automorphic functions
Download or read book Introductory Lectures on Siegel Modular Forms written by Helmut Klingen and published by Cambridge University Press. This book was released on 1990-02-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Automorphic Forms and Even Unimodular Lattices written by Gaëtan Chenevier and published by Springer. This book was released on 2019-02-28 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Download or read book Siegel Modular Forms written by Ameya Pitale and published by Springer. This book was released on 2019-05-07 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Download or read book Relative Trace Formulas written by Werner Müller and published by Springer. This book was released on 2022-05-20 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.
Download or read book The Abel Prize 2013 2017 written by Helge Holden and published by Springer. This book was released on 2019-02-23 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Particle Physics Reference Library written by Christian W. Fabjan and published by Springer Nature. This book was released on 2020 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the "Particle Physics Reference Library" provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A, B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access
Download or read book Sampling Techniques for Supervised or Unsupervised Tasks written by Frédéric Ros and published by Springer Nature. This book was released on 2019-10-26 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail sampling techniques that can be used for unsupervised and supervised cases, with a focus on sampling techniques for machine learning algorithms. It covers theory and models of sampling methods for managing scalability and the “curse of dimensionality”, their implementations, evaluations, and applications. A large part of the book is dedicated to database comprising standard feature vectors, and a special section is reserved to the handling of more complex objects and dynamic scenarios. The book is ideal for anyone teaching or learning pattern recognition and interesting teaching or learning pattern recognition and is interested in the big data challenge. It provides an accessible introduction to the field and discusses the state of the art concerning sampling techniques for supervised and unsupervised task. Provides a comprehensive description of sampling techniques for unsupervised and supervised tasks; Describe implementation and evaluation of algorithms that simultaneously manage scalable problems and curse of dimensionality; Addresses the role of sampling in dynamic scenarios, sampling when dealing with complex objects, and new challenges arising from big data. "This book represents a timely collection of state-of-the art research of sampling techniques, suitable for anyone who wants to become more familiar with these helpful techniques for tackling the big data challenge." M. Emre Celebi, Ph.D., Professor and Chair, Department of Computer Science, University of Central Arkansas "In science the difficulty is not to have ideas, but it is to make them work" From Carlo Rovelli
Download or read book The Theory of Jacobi Forms written by Martin Eichler and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Evanescent Waves in Optics written by Mario Bertolotti and published by Springer. This book was released on 2017-10-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introductory discussion of evanescent waves and plasmons, describes their properties and uses, and shows how they are fundamental when operating with nanoscale optics. Far field optics is not suitable for the design, description, and operation of devices at this nanometre scale. Instead one must work with models based on near-field optics and surface evanescent waves. The new discipline of plasmonics has grown to encompass the generation and application of plasmons both as a travelling excitation in a nanostructure and as a stationary enhancement of the electrical field near metal nanosurfaces. The book begins with a brief review of the basic concepts of electromagnetism, then introduces evanescent waves through reflection and refraction, and shows how they appear in diffraction problems, before discussing the role that they play in optical waveguides and sensors. The application of evanescent waves in super-resolution devices is briefly presented, before plasmons are introduced. The surface plasmon polaritons (SPPs) are then treated, highlighting their potential applications also in ultra-compact circuitry. The book concludes with a discussion of the quantization of evanescent waves and quantum information processing. The book is intended for students and researchers who wish to enter the field or to have some insight into the matter. It is not a textbook but simply an introduction to more complete and in-depth discussions. The field of plasmonics has exploded in the last ten years, and most of the material treated in this book is scattered in original or review papers. A short comprehensive treatment is missing; this book is intended to provide just that.
Download or read book Modular Forms and Hecke Operators written by A. N. Andrianov and published by American Mathematical Soc.. This book was released on 2016-01-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.
Download or read book Algebraic Methods in General Rough Sets written by A. Mani and published by Springer. This book was released on 2019-01-11 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.
Download or read book Control and System Theory of Discrete Time Stochastic Systems written by Jan H. van Schuppen and published by Springer Nature. This book was released on 2021-08-02 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Imaging Biomarkers written by Luis Martí-Bonmatí and published by Springer. This book was released on 2016-11-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Automorphic Forms written by Bernhard Heim and published by Springer. This book was released on 2014-11-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 “International Conference on Automorphic Forms and Number Theory,” held in Muscat, Sultanate of Oman. The present volume includes original research as well as some surveys and outlines of research altogether providing a contemporary snapshot on the latest activities in the field and covering the topics of: Borcherds products Congruences and Codes Jacobi forms Siegel and Hermitian modular forms Special values of L-series Recently, the Sultanate of Oman became a member of the International Mathematical Society. In view of this development, the conference provided the platform for scientific exchange and collaboration between scientists of different countries from all over the world. In particular, an opportunity was established for a close exchange between scientists and students of Germany, Oman, and Japan. The conference was hosted by the Sultan Qaboos University and the German University of Technology in Oman.
