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Professor Motohashi shows that the Riemann zeta function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the function itself.
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This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several... Læs mere
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This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Graduate students and non-specialists will find this an up-to-date and accessible introduction.
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Dr Smithies analyses the process whereby Cauchy created one of the most important branch of mathematics discovered in the nineteenth century. It is the... Læs mere
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The techniques used to solve non-linear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems from first principles,... Læs mere
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This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models... Læs mere
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Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, conformal dynamics, discrete groups, algebraic curves and... Læs mere
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First published in 2000, this book provides a clear and complete picture of research in Several Complex Variables and its interactions with PDEs, algebraic geometry, number... Læs mere
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This 2006 treatment of Jacobi elliptic functions seeks to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the... Læs mere
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Using modern methods from computational group theory and representation theory, this book addresses a classical topic in the theory of complex functions. It is suitable for graduate students and researchers.
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This book presents a way of learning and teaching a subject at the heart of much of pure and applied mathematics, physics, engineering and even art. The book lets... Læs mere
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L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This... Læs mere