The Heat Kernel and Theta Inversion - E-book

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The Heat Kernel And Theta Inversion On Sl2(c) - ENG

Jay Jorgenson; Serge Lang

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Sinopsis

ISBN:	9780387380322
Formato:	ePub
Idioma:	Inglés
Editorial:	Springer Nature
Tema:	Matemáticas
Subtema:	Teoría dos Números
Año de publicación:	2009-02-20

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 authors previous work, the inversion formula then leads to zeta functions through the Gauss transform.

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