1. CJM 2011 (vol 64 pp. 588)
2. CJM 2009 (vol 62 pp. 456)
 Yang, Tonghai

The ChowlaâSelberg Formula and The Colmez Conjecture
In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
Categories:11G15, 11F41, 14K22 

3. CJM 2009 (vol 61 pp. 395)
 Moriyama, Tomonori

$L$Functions for $\GSp(2)\times \GL(2)$: Archimedean Theory and Applications
Let $\Pi$ be a generic cuspidal automorphic representation of
$\GSp(2)$ defined over a totally real algebraic number field $\gfk$
whose archimedean type is either a (limit of) large discrete series
representation or a certain principal series representation. Through
explicit computation of archimedean local zeta integrals, we prove the
functional equation of tensor product $L$functions $L(s,\Pi \times
\sigma)$ for an arbitrary cuspidal automorphic representation $\sigma$
of $\GL(2)$. We also give an application to the spinor $L$function
of $\Pi$.
Categories:11F70, 11F41, 11F46 
