Heat Eisenstein Series On Sl N
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Heat Eisenstein Series on $\mathrm {SL}_n(C)$
Author: Jay Jorgenson
language: en
Publisher: American Mathematical Soc.
Release Date: 2009
The purpose of this Memoir is to define and study multi-variable Eisenstein series attached to heat kernels. Fundamental properties of heat Eisenstein series are proved, and conjectural behavior, including their role in spectral expansions, are stated.
Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
Author: Marco Bramanti
language: en
Publisher: American Mathematical Soc.
Release Date: 2010
"March 2010, Volume 204, number 961 (end of volume)."
The Heat Kernel and Theta Inversion on SL2(C)
Author: Jay Jorgenson
language: en
Publisher: Springer Science & Business Media
Release Date: 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 author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./