The Heat Kernel and Theta Inversion on SL2(C)

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book The Heat Kernel and Theta Inversion on SL2(C) by Jay Jorgenson, Serge Lang, Springer New York
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Author: Jay Jorgenson, Serge Lang ISBN: 9780387380322
Publisher: Springer New York Publication: February 20, 2009
Imprint: Springer Language: English
Author: Jay Jorgenson, Serge Lang
ISBN: 9780387380322
Publisher: Springer New York
Publication: February 20, 2009
Imprint: Springer
Language: English

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.

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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.

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