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Cover: 9780387380315 | The Heat Kernel and Theta Inversion on SL2(C) | Serge Lang (u. a.) | X
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The Heat Kernel and Theta Inversion on SL2(C)
Buch von Serge Lang (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

The 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 gotten 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.

Inhaltsverzeichnis
Gaussians, 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.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Monographs in Mathematics
Inhalt: x
319 S.
Approx. 410 p.
ISBN-13: 9780387380315
ISBN-10: 0387380310
Sprache: Englisch
Herstellernummer: 11604488
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Jorgenson, Jay
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Monographs in Mathematics
Maße: 241 x 160 x 23 mm
Von/Mit: Serge Lang (u. a.)
Erscheinungsdatum: 15.10.2008
Gewicht: 0,664 kg
Artikel-ID: 101982116
Zusammenfassung

The 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 gotten 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.

Inhaltsverzeichnis
Gaussians, 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.
Details
Erscheinungsjahr: 2008
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Monographs in Mathematics
Inhalt: x
319 S.
Approx. 410 p.
ISBN-13: 9780387380315
ISBN-10: 0387380310
Sprache: Englisch
Herstellernummer: 11604488
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Lang, Serge
Jorgenson, Jay
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Monographs in Mathematics
Maße: 241 x 160 x 23 mm
Von/Mit: Serge Lang (u. a.)
Erscheinungsdatum: 15.10.2008
Gewicht: 0,664 kg
Artikel-ID: 101982116
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