000			02903nam a22003498i 4500
001			CR9780511662331
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			091215s1993||||enk o ||1 0|eng|d
020			_a9780511662331 (ebook)
020			_z9780521448048 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA351 _b.Y85 1993
082	0	0	_a515/.56 _220
100	1		_aYukie, Akihiko, _eauthor.
245	1	0	_aShintani zeta functions / _cAkihiko Yukie.
264		1	_aCambridge : _bCambridge University Press, _c1993.
300			_a1 online resource (xii, 339 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v183
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_apt. I. The general theory. Ch. 1. Preliminaries. Ch. 2. Eisenstein series on GL(n). Ch. 3. The general program -- pt. II. The Siegel-Shintani case. Ch. 4. The zeta function for the space of quadratic forms -- pt. III. Preliminaries for the quartic case. Ch. 5. The case G = GL(2) x GL(2), V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2]. Ch. 6. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k. Ch. 7. The case G = GL(2) x GL(1)[superscript 2], V = Sym[superscript 2]k[superscript 2] [actual symbol not reproducible] k[superscript 2] -- pt. IV. The quartic case. Ch. 8. Invariant theory of pairs of ternary quadratic forms. Ch. 9. Preliminary estimates. Ch. 10. The non-constant terms associated with unstable strata. Ch. 11. Unstable distributions. Ch. 12. Contributions front unstable strata. Ch. 13. The main theorem.
520			_aThe theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory.
650		0	_aFunctions, Zeta.
776	0	8	_iPrint version: _z9780521448048
830		0	_aLondon Mathematical Society lecture note series ; _v183.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511662331
999			_c517825 _d517823