000			03658nam a22005295i 4500
001			978-0-387-38032-2
003			DE-He213
005			20161121231206.0
007			cr nn 008mamaa
008			100301s2008 xxu| s |||| 0|eng d
020			_a9780387380322 _9978-0-387-38032-2
024	7		_a10.1007/978-0-387-38032-2 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aJorgenson, Jay. _eauthor.
245	1	4	_aThe Heat Kernel and Theta Inversion on SL2(C) _h[electronic resource] / _cby Jay Jorgenson, Serge Lang.
264		1	_aNew York, NY : _bSpringer New York, _c2008.
300			_aX, 319 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_aGaussians, Spherical Inversion, and the Heat Kernel -- Spherical Inversion on SL2(C) -- The Heat Gaussian and Heat Kernel -- QED, LEG, Transpose, and Casimir -- Enter ?: The General Trace Formula -- Convergence and Divergence of the Selberg Trace -- The Cuspidal and Noncuspidal Traces -- The Heat Kernel on ?\G/K -- The Fundamental Domain -- ?-Periodization of the Heat Kernel -- Heat Kernel Convolution on (?\G/K) -- Fourier-Eisenstein Eigenfunction Expansions -- The Tube Domain for ?? -- The ?/U-Fourier Expansion of Eisenstein Series -- Adjointness Formula and the ?\G-Eigenfunction Expansion -- The Eisenstein-Cuspidal Affair -- The Eisenstein Y-Asymptotics -- The Cuspidal Trace Y-Asymptotics -- Analytic Evaluations.
520			_aThe present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side. By focusing on the case of SL2(Z[i]) acting on SL2(C), the authors are able to emphasize the importance of specific examples of the general theory of the general Selberg trace formula and uncover the second step in their envisioned "ladder" of geometrically defined zeta functions, where each conjectured step would include lower level zeta functions as factors in functional equations.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aGroup theory.
650		0	_aMathematical analysis.
650		0	_aAnalysis (Mathematics).
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aAlgebra.
650	2	4	_aAnalysis.
700	1		_aLang, Serge. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387380315
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-38032-2
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c509907 _d509907