Spectral Theory of the Riemann Zeta-Function, Motohashi

Автор: Coates
Название: The Bloch–Kato Conjecture for the Riemann Zeta Function
ISBN: 1107492963 ISBN-13(EAN): 9781107492967
Издательство: Cambridge Academ
Рейтинг:
Цена: 9029.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: An account of a significant body of recent work that resolves some long-standing mysteries concerning special values of the Riemann zeta function. It brings together many important results from K-theory, motivic cohomology, and Iwasawa theory, accessible at graduate level and above.

Автор: Hislop
Название: Introduction to Spectral Theory
ISBN: 0387945016 ISBN-13(EAN): 9780387945019
Издательство: Springer
Рейтинг:
Цена: 23757.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This work aims to introduce students to active areas of research in mathematical physics in a rather direct way, thus minimizing the use of abstract mathematics. The book`s main features are geometric methods in spectral analysis, semi-classical analysis of resonance and other topics.

Автор: Bobenko
Название: Computational Approach to Riemann Surfaces
ISBN: 3642174124 ISBN-13(EAN): 9783642174124
Издательство: Springer
Рейтинг:
Цена: 6282.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Автор: Borthwick
Название: Spectral Theory of Infinite-Area Hyperbolic Surfaces
ISBN: 3319338757 ISBN-13(EAN): 9783319338750
Издательство: Springer
Рейтинг:
Цена: 15372.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added.Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution.The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition:'The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it.' (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)