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The Heat Kernel and Theta Inversion on SL2(C). 2008 ed..
・ISBN 978-0-387-38031-5 hard EUR 99.99
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| 著者・編者 | Jorgenson, Jay / Lang, Serge, |
|---|---|
| シリーズ | Springer Monographs in Mathematics |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2008 |
| ページ数 | 319 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-19298＞ |
解説
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.