000 04125nam a22005535i 4500
001 978-0-387-38032-2
003 DE-He213
005 20181204133001.0
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
040 _aISI Library, Kolkata
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 _aJorgenson, Jay.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
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 _aNumber theory.
650 0 _aGroup theory.
650 0 _aAlgebra.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aGroup Theory and Generalizations.
_0http://scigraph.springernature.com/things/product-market-codes/M11078
650 2 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
700 1 _aLang, Serge.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387564050
776 0 8 _iPrinted edition:
_z9781441922823
776 0 8 _iPrinted edition:
_z9780387380315
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttps://doi.org/10.1007/978-0-387-38032-2
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425736
_d425736