MARC Record from marc_columbia

LEADER: 03699cam a2200361 a 4500
001 7094605
005 20221130205832.0
008 061206t20082008nyua b 001 0 eng
020 $a9780387380315 (hbk.)
020 $a0387380310 (hbk.)
024 $a40016254147
035 $a(OCoLC)ocm77795761\
035 $a(OCoLC)77795761
035 $a(NNC)7094605
035 $a7094605
040 $aUKM$cUKM$dBAKER$dBTCTA$dYDXCP$dOCLCG$dBWX$dOCLCQ$dOrLoB-B
050 4 $aQA331$b.J67 2008
082 04 $a515/.7$222
100 1 $aJorgenson, Jay.$0http://id.loc.gov/authorities/names/n93099435
245 14 $aThe heat kernel and theta inversion on SL₂(C) /$cJay Jorgenson, Serge Lang.
260 $aNew York :$bSpringer,$c[2008], ©2008.
300 $ax, 319 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aSpringer monographs in mathematics
504 $aIncludes bibliographical references (p. 311-315) and index.
505 00 $gPt. I.$tGaussians, Spherical Inversion, and the Heat Kernel -- $g1.$tSpherical Inversion on SL[subscript 2](C) -- $g2.$tThe Heat Gaussian and Heat Kernel -- $g3.$tQED, LEG, Transpose, and Casimir -- $gPt. II.$tEnter [Gamma]: The General Trace Formula -- $g4.$tConvergence and Divergence of the Selberg Trace -- $g5.$tThe Cuspidal and Noncuspidal Traces -- $gPt. III.$tThe Heat Kernel on [Gamma]\G/K -- $g6.$tThe Fundamental Domain -- $g7.$t[Gamma]-Periodization of the Heat Kernel -- $g8.$tHeat Kernel Convolution on L[superscript 2][subscript cusp] ([Gamma]\G/K) -- $gPt. IV.$tFourier-Eisenstein Eigenfunction Expansions -- $g9.$tThe Tube Domain for [Gamma][infinity] -- $g10.$tThe [Gamma][subscript U]\U-Fourier Expansion of Eisenstein Series -- $g11.$tAdjointness Formula and the [Gamma]\G-Eigenfunction Expansion -- $gPt. V.$tThe Eisenstein - Cuspidal Affiar -- $g12.$tThe Eisenstein Y-Asymptotics -- $g13.$tThe Cuspidal Trace Y-Asymptotics -- $g14.$tAnalytic Evaluations.
520 1 $a"The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL[subscript 2](C). The authors begin with the realization of the heat kernel on SL[subscript 2](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 SL[subscript 2](Z[i]) acting on SL[subscript 2](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."--BOOK JACKET.
650 0 $aKernel functions.$0http://id.loc.gov/authorities/subjects/sh85072061
650 0 $aFunctions, Theta.$0http://id.loc.gov/authorities/subjects/sh85052352
700 1 $aLang, Serge,$d1927-2005.$0http://id.loc.gov/authorities/names/n79053939
830 0 $aSpringer monographs in mathematics.$0http://id.loc.gov/authorities/names/n97101238
852 00 $bmat$hQA331$i.J67 2008g