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Matrix String Partition Functions
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We evaluate quasi-classically the Ramond partition function of Euclidean D=10 U(N) super-Yang--Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasi-classical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasi-classical calculation might be exact.
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Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
Minimal and next-to-minimal automorphic functions on split simply-laced groups are uniquely determined by, and explicitly reconstructible from, their Whittaker coefficients.
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