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.
- ISBN13 9780387380315
- Publish Date 15 October 2008 (first published 1 January 2008)
- Publish Status Active
- Publish Country US
- Imprint Springer-Verlag New York Inc.
- Edition 2008 ed.
- Format Hardcover
- Pages 319
- Language English