Area, Lattice Points, and Exponential Sums (London Mathematical Society Monographs)

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9780198534662: Area, Lattice Points, and Exponential Sums (London Mathematical Society Monographs)

In analytic number theory many problems can be "reduced" to those involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method for estimating the Riemann zeta function. Huxley and his coworkers have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput's method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The book will find its biggest readership among mathematics graduate students and academics with a research interest in analytic theory; specifically exponential sum methods.

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About the Author:

M. N. Huxley is at University of Wales, Cardiff.

Review:

`This book [is] very detailed ... The book is very well written. It is an excellent and important work for all mathematicians who deal with exponential sums and lattice point theory. It is accessible to graduate students beginning research.' Zentrallblat fur Mathematik, vol. 861, 1997

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Book Description Oxford University Press, United Kingdom, 1996. Hardback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. In analytic number theory a large number of problems can be reduced to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput s method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background. Bookseller Inventory # APC9780198534662

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Book Description Oxford University Press, United Kingdom, 1996. Hardback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.In analytic number theory a large number of problems can be reduced to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput s method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background. Bookseller Inventory # APC9780198534662

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