caa a22 4500 445387246 CHVBK 20180317143035.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10714-011-1175-9 doi (NATIONALLICENCE)springer-10.1007/s10714-011-1175-9 Sen Ashoke Harish-Chandra Research Institute, Chhatnag Road, Jhusi, 211019, Allahabad, India aut How do black holes predict the sign of the Fourier coefficients of siegel modular forms? [Elektronische Daten] [Ashoke Sen] Single centered supersymmetric black holes in four dimensions have spherically symmetric horizon and hence carry zero angular momentum. This leads to a specific sign of the helicity trace index associated with these black holes. Since the latter are given by the Fourier expansion coefficients of appropriate meromorphic modular forms of $${Sp(2,{\mathbb{Z}})}$$ or its subgroup, we are led to a specific prediction for the signs of a subset of these Fourier coefficients which represent contributions from single centered black holes only. We explicitly test these predictions for the modular forms which compute the index of quarter BPS black holes in heterotic string theory on T 6, as well as in $${{\mathbb{Z}}_N}$$ CHL models for N=2, 3, 5, 7. Springer Science+Business Media, LLC, 2011 Black holes nationallicence String theory nationallicence Siegel modular forms nationallicence General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/8(2011-08-01), 2171-2183 0001-7701 43:8<2171 2011 43 10714 https://doi.org/10.1007/s10714-011-1175-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-011-1175-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sen Ashoke Harish-Chandra Research Institute, Chhatnag Road, Jhusi, 211019, Allahabad, India aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/8(2011-08-01), 2171-2183 0001-7701 43:8<2171 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer