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Faltings heights of CM elliptic curves and special Gamma values
In this paper, we evaluate the Faltings height of an elliptic curve with complex multiplication by an order in an imaginary quadratic field in terms of Euler’s Gamma function at rational arguments.
On the Colmez conjecture for non-abelian CM fields
The Colmez conjecture relates the Faltings height of an abelian variety with complex multiplication by the ring of integers of a CM field E to logarithmic derivatives of Artin L-functions at s=0. In this paper, we prove ...
The Chowla-Selberg formula for abelian CM fields and Faltings heights
In this paper we establish a Chowla-Selberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Euler’s gamma function Γ and an analogous function ...
The asymptotic distribution of Andrews’ smallest parts function
In this paper, we use methods from the spectral theory of automorphic forms to give an asymptotic formula with a power saving error term for Andrews’ smallest parts function spt(n). We use this formula to deduce an asymptotic ...