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A classical result from analytic number theory by Rademacher gives an exact formula for the Fourier coefficients of modular forms of non-positive weight.
1904
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T. Hartman, D. Mazac and L. Rastelli, Sphere Packing and Quantum Gravity, JHEP
1905
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1906
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1906
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1910
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S. Pal and Z. Sun, Tauberian-Cardy formula with spin,
1910
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G. Hardy and S. Ramanujan, Asymptotic Formulæ in Combinatory Analysis, Proc. London Math. Soc
1918
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H. Rademacher, A Convergent Series for the Partition Function p(n), Proc. Natl. Acad. Sci. U.S.A
1937
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H. Rademacher, The Fourier Coefficients of the Modular Invariant J ( τ ) J(\tau) , American Journal of Mathematics
1938
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H. Rademacher and H. S. Zuckerman, On the Fourier Coefficients of Certain Modular Forms of Positive Dimension, Annals of Mathematics, Second Series
1938
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H. Rademacher, On the Expansion of the Partition Function in a Series, Annals of Mathematics, Second Series,
1943
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H. Rademacher, Lectures on Analytic Number Theory, Tata Institute of Fundamental Research, Bombay
1954
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E. Wright, Stacks. II. Quarterly. J. Math
1971
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J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys
1986
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A. Strominger, Black hole entropy from near horizon microstates, JHEP
1998
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A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP
2010
2014
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2014
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C. A. Keller and A. Maloney, Poincare Series, 3D Gravity and CFT Spectroscopy, JHEP
2015
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H. Ngo and R. Rhoades, Integer partitions, probabilities and quantum modular forms, Res. Math. Sci
2017
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J. Bae, S. Lee, and J. Song, Modular Constraints on Conformal Field Theories with Currents, JHEP
2017
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Cited alongside, same era.
J. F. Duncan and I. B. Frenkel, Rademacher sums, Moonshine and Gravity, Commun. Num. Theor. Phys
2011
Cited alongside, same era.
S. Hellerman, A Universal Inequality for CFT and Quantum Gravity, JHEP
2011
Cited alongside, same era.
D. Friedan and C. A. Keller, Constraints on 2d CFT partition functions, JHEP
2013
Cited alongside, same era.
R. Dijkgraaf, J. M. Maldacena, G. W. Moore and E. P. Verlinde, A Black hole Farey tail,
Cited in the paper.
F. Brown, A class of non-holomorphic modular forms I,
Cited in the paper.
N. Benjamin, S. Collier, and A. Maloney, to appear
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2018
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S. Collier, Y. H. Lin and X. Yin, Modular Bootstrap Revisited, JHEP
2018
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2019
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