ISBN: 9780387380322

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 SL2(C). T… More...

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 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., Springer<

ISBN: 9780387380322

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of th… More...

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform.; PDF; Scientific, Technical and Medical > Mathematics > Number theory, Springer New York<

ISBN: 9780387380322

*The Heat Kernel and Theta Inversion on SL2(C)* / pdf eBook für 96.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachth… More...

*The Heat Kernel and Theta Inversion on SL2(C)* / pdf eBook für 96.49 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Mathematik Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Mathematik, Springer-Verlag GmbH<

ISBN: 9780387380322

The Heat Kernel and Theta Inversion on SL2(C): ab 96.49 € eBooks > Fachthemen & Wissenschaft > Mathematik Springer-Verlag GmbH eBook als pdf, Springer-Verlag GmbH

2009, ISBN: 9780387380322

eBooks, eBook Download (PDF), 2008, [PU: Springer New York], Springer New York, 2009