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Siegel Modular Forms and Black Hole Entropy

Alexandre Belin, Alejandra Castro, Joao Gomes, Christoph A. Keller

14/11/16 Published in : arXiv:1611.04588

We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form \chi_{10} in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case. We implement this counting for other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes. We investigate the growth of their coefficients, identifying the dominant contributions and the leading logarithmic corrections in various regimes. We also discuss similarities and differences to the behavior of \chi_{10}, and possible physical interpretations of such forms both from a microscopic and gravitational point of view.

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Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum

Regularization of divergent integrals

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