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Spectral theory of the Riemann zeta-...

Motohashi, Y.

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Spectral theory of the Riemann zeta-function

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral theory of the Riemann zeta-function/ Yoichi Motohashi.
Author:	Motohashi, Y.
Published:	Cambridge :Cambridge University Press, : 1997.,
Description:	ix, 228 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics.
Subject:	Functions, Zeta. -
Online resource:	https://doi.org/10.1017/CBO9780511983399
ISBN:	9780511983399

Spectral theory of the Riemann zeta-function
Motohashi, Y.

Spectral theory of the Riemann zeta-function[electronic resource] /Yoichi Motohashi. - Cambridge :Cambridge University Press,1997. - ix, 228 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;127. - Cambridge tracts in mathematics ;127..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics.

The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the 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 zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.

ISBN: 9780511983399Subjects--Topical Terms:

558393
Functions, Zeta.

LC Class. No.: QA246 / .M78 1997

Dewey Class. No.: 512.73

Spectral theory of the Riemann zeta-function
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245 1 0 $a Spectral theory of the Riemann zeta-function $h [electronic resource] / $c Yoichi Motohashi.
260 $a Cambridge : $b Cambridge University Press, $c 1997.
300 $a ix, 228 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 127
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Convention and assumed background -- 1. Non-Euclidean harmonics -- 2. Trace formulas -- 3. Automorphic L-functions -- 4. An explicit formula -- 5. Asymptotics.
520 $a The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the 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 zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.
650 0 $a Functions, Zeta. $3 558393
650 0 $a Spectral theory (Mathematics) $3 524915
830 0 $a Cambridge tracts in mathematics ; $v 127. $3 3470701
856 4 0 $u https://doi.org/10.1017/CBO9780511983399