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This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes: (I) The correspondence between the forms of half-integral weight and those of integral weight. (II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight. Goro Shimura is currently a professor emeritus of mathematics at Princeton University.

Numerical analysis --- numerieke analyse

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Advances in the development of parallel algorithms and system software now enable the ever-increasing power of scalable high-performance computers to be harnessed for scientific computing applications at fidelities that rival - and in many cases exceed - experimental methodologies. This comprehensive text/reference, inspired by the visionary work of Prof. Ahmed H. Sameh, represents the state of the art in parallel numerical algorithms, applications, architectures, and system software. Articles in this collection address solutions to various challenges arising from concurrency, scale, energy efficiency, and programmability. These solutions are discussed in the context of diverse applications, ranging from scientific simulations to large-scale data analysis and mining. Topics and features: Includes contributions from an international selection of world-class authorities, inspired by the work of Prof. Ahmed H. Sameh Examines various aspects of parallel algorithm-architecture interaction through articles on computational capacity-based codesign and automatic restructuring of programs using compilation techniques Reviews emerging applications of numerical methods in information retrieval and data mining Discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems Presents outstanding challenges and developing technologies, and puts these in their historical context This authoritative reference is a must-read for researchers and graduate students in disciplines as diverse as computational fluid dynamics, signal processing, and structural mechanics. Professionals involved in applications that rely on high-performance computers will also find the text an essential resource.

Information systems --- Computer. Automation --- IR (information retrieval) --- wiskunde --- numerieke analyse

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This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some advantages over more commonly used turbulence models - as well as some disadvantages. Our goal in this book is to provide a clear and complete mathematical development of ADMs, while pointing out the difficulties that remain. In order to do so, we present the analytical theory of ADMs, along with its connections, motivations and complements in the phenomenology of and algorithms for ADMs.

Numerical analysis --- Fluid mechanics --- ingenieurswetenschappen --- numerieke analyse --- vloeistoffen

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Information systems --- Computer. Automation --- IR (information retrieval) --- wiskunde --- numerieke analyse

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Numerical analysis --- Fluid mechanics --- ingenieurswetenschappen --- numerieke analyse --- vloeistoffen