Trace formulas for a class of compact complex surfaces

Details Trace formulas for a class of compact complex surfaces Trace formulas for a class of compact complex surfaces

2001-08-27

arxiv.org/abs/math/0108178v1

Mathematics

Number Theory

63 pages

Scientific paper

We give the trace formulas of weight $k$ for cocompact, torsion-free discrete
subgroups of $SU(2, 1)$ and prove the analogue of the Riemann hypothesis on
compact complex surfaces $M$ with $c_1^2(M)=3 c_2(M)$, where $c_i(M)$ is the
$i$-th Chern class of $M$, $c_2(M)$ is a multiple of three and $c_2(M)>0$.

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