000			03239nam a22004575i 4500
001			978-3-319-95891-0
003			DE-He213
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008			190228s2019 gw | o |||| 0|eng d
020			_a9783319958910
024	7		_a10.1007/978-3-319-95891-0 _2doi
040			_ceng
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
072		7	_aPBH _2thema
082	0	4	_a512.7 _223
100	1		_aChenevier, Gaëtan. _eauthor.
245	1	0	_aAutomorphic Forms and Even Unimodular Lattices _bKneser Neighbors of Niemeier Lattices / _cby Gaëtan Chenevier, Jean Lannes.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2019.
300			_aXXI, 417 p. 24 illus., 1 illus. in color.
336			_atext _btxt _2rdacontent.
337			_acomputer _bc _2rdamedia.
338			_aonline resource _bcr _2rdacarrier.
347			_atext file _bPDF _2rda.
490	1		_aErgebnisse der Mathematik und ihrer Grenzgebiete ; _vFolge 3, Band 69.
505	0		_aPreface.-1 Introduction -- 2 Bilinear and Quadratic Algebra -- 3 Kneser Neighbors -- 4 Automorphic Forms and Hecke Operators -- 5 Theta Series and Even Unimodular Lattices -- 6 Langlands Parametrization -- 7 A Few Cases of the Arthur–Langlands Conjecture -- 8 Arthur's Classification for the Classical Z-groups -- 9 Proofs of the Main Theorems -- 10 Applications -- A The Barnes–Wall Lattice and the Siegel Theta Series -- B Quadratic Forms and Neighbors in Odd Dimension -- C Tables -- References.-.Postface- Notation Index.-Terminology Index.
506			_aAccess restricted to subscribing institutions.
520			_aThis book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
538			_aMode of access: World Wide Web.
650		0	_aNumber theory.
650		0	_aAlgebra.
700	1		_aLannes, Jean. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks.
830		0	_aErgebnisse der Mathematik und ihrer Grenzgebiete. _p3. Folge ; _vBd. 69.
856	4	0	_uhttps://ezproxy.lib.gla.ac.uk/login?url=https://doi.org/10.1007/978-3-319-95891-0 _zConnect to resource
907			_a.b33398690
942			_2ddc _cCART _n0
999			_c36810 _d36810