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Shintani Zeta Functions

Author: Akihiko Yukie
Publisher: Cambridge : Cambridge University Press, 1994.
Series: London Mathematical Society lecture note series, no. 183.
Edition/Format:   eBook : Document : English
Summary:
This is amongst the first books on the theory of prehomogeneous vector spaces, and represents the author's deep study of the subject.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Akihiko Yukie
ISBN: 9780511662331 0511662335 9780521448048 0521448042 9781107366862 1107366860
OCLC Number: 776965662
Notes: Title from publishers bibliographic system (viewed 22 Dec 2011).
Description: 1 online resource (352 pages).
Contents: Cover --
Title --
Copyright --
Dedication --
Table of contents --
Preface --
Notation --
Introduction --
0.1 What is a prehomogeneous vector space? --
0.2 The classification --
0.3 The global zeta function --
0.4 The orbit space Gk \ Vkss --
0.5 The filtering process and the local theory: a note by D. Wright --
0.6 The outline of the general procedure --
Part I The general theory --
Chapter 1 Preliminaries --
1.1 An invariant measure on GL(n) --
1.2 Some adelic analysis --
Chapter 2 Eisenstein series on GL(n) --
2.1 The Fourier expansion of automorphic forms on GL(n) 2.2 The constant terms of Eisenstein series on GL(n) --
2.3 The Whittaker functions --
2.4 The Fourier expansion of Eisenstein series on GL(n) --
Chapter 3 The general program --
3.1 The zeta function --
3.2 The Morse stratification --
3.3 The paths --
3.4 Shintani's lemma for GL(n) --
3.5 The general process --
3.6 The passing principle --
3.7 Wright's principle --
3.8 Examples --
Part II The Siegel-Shintani case --
Chapter 4 The zeta function for the space of quadratic forms --
4.1 The space of quadratic forms --
4.2 The case n = 2 --
4.3 <U+00dd>-sequences. 4.4 An inductive formulation --
4.5 Paths in B1 --
4.6 Paths in B3,B4 --
4.7 The cancellations --
4.8 The work of Siegel and Shintani --
Part III Preliminaries for the quartic case --
Chapter 5 The case G = GL(2) x GL(2), V = Sym2k2 O k2 --
5.1 The space Sym2k2 O k2 --
5.2 The adjusting term --
5.3 Contributions from <U+0065>1, <U+0065>3 --
5.4 Contributions from <U+0065>2, <U+0065>4 --
5.5 The contribution from Vssstk --
5.6 The principal part formula --
Chapter 6 The case G = GL(2) x GL(1)2, V = Sym2k2 O k --
6.1 Reducible prehomogeneous vector spaces with two irreducible factors. 6.2 The spaces Sym2k2 O k, Sym2k2 O k2 --
6.3 The principal part formula --
Chapter 7 The case G = GL(2) x GL(1)2, V = Sym2k2 O k2 --
7.1 Unstable distributions --
7.2 Contributions from unstable strata --
7.3 The principal part formulaWe define --
Part IV The quartic case --
Chapter 8 Invariant theory of pairs of ternary quadratic forms --
8.1 The space of pairs of ternary quadratic forms --
8.2 The Morse stratification --
8.3 <U+00dd>-sequences of lengths {601} 2 --
Chapter 9 Preliminary estimates --
9.1 Distributions associated with paths --
9.2 The smoothed Eisenstein series. Chapter 10 The non-constant terms associated with unstable strata --
10.1 The case <U+0065> = (<U+00dd>4) --
10.2 The cases <U+0065> = (<U+00dd>5), (<U+00dd>10, <U+00dd>10,1) --
10.3 The cases <U+0065> = (<U+00dd>6), (<U+00dd>8, <U+00dd>8,1) --
10.4 The case <U+0065> = (<U+00dd>7) --
10.5 The case <U+0065> = (<U+00dd>8) --
10.6 The cases <U+0065> = (<U+00dd>8, <U+00dd>8,2), (<U+00dd>9) --
Chapter 11 Unstable distributions --
11.1 Unstable distributions --
11.2 Technical lemmas --
Chapter 12 Contributions from unstable strata --
12.1 The case <U+0065> = (<U+00dd>1) --
12.2 The case <U+0065> = (<U+00dd>2) --
12.3 The case <U+0065> = (<U+00dd>3) --
12.4 The case <U+0065> = (<U+00dd>4) --
12.5 The case <U+0065> = (<U+00dd>5) --
12.6 The case <U+0065> = (<U+00dd>6)
Series Title: London Mathematical Society lecture note series, no. 183.
Responsibility: Akihiko Yukie.

Abstract:

This is amongst the first books on the theory of prehomogeneous vector spaces, and represents the author's deep study of the subject.  Read more...

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