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We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms.
Fonctions modulaires et fonctions fuchsiennes
H. Poincaré · 1911
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On two theorems of combinatory analysis and some allied identities
L. J. Rogers · 1917
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Theorie der automorphen Formen beliebiger reeller Dimension und ihre Darstellung durch eine neue Art Poincaréscher Reihen
Hans Petersson · 1930
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Über die Entwicklungskoeffizienten der automorphen Formen
Hans Petersson · 1932
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Über die Entwicklungskoeffizienten einer allgemeinen Klasse automorpher Formen
Hans Petersson · 1933
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On the Partition Function p ( n ) p(n)
Hans Rademacher · 1937
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The Fourier Coefficients of the Modular Invariant J( τ \tau )
Hans Rademacher · 1938
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On the Fourier coefficients of certain modular forms of positive dimension
Hans Rademacher and Herbert S. Zuckerman · 1938
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The Fourier Series and the Functional Equation of the Absolute Modular Invariant J( τ \tau )
Hans Rademacher · 1939
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Construction of a class of modular functions and forms
Marvin Isadore Knopp · 1961
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Construction of a class of modular functions and forms. II
Marvin Isadore Knopp · 1961
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Construction of automorphic forms on H H -groups and supplementary Fourier series
Marvin Isadore Knopp · 1962
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On abelian integrals of the second kind and modular functions
Marvin Isadore Knopp · 1962
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On the estimation of Fourier coefficients of modular forms
Atle Selberg · 1965
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Introduction to the arithmetic theory of automorphic functions
Goro Shimura · 1971
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Construction of automorphic forms and integrals
Douglas Niebur · 1974
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Monstrous Moonshine
J. H. Conway and S. P. Norton · 1979
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Finite groups and modular functions
J. G. Thompson · 1979
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Some numerology between the Fischer-Griess Monster and the elliptic modular function
J. G. Thompson · 1979
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Ramunujan’s “lost” notebook. III. The Rogers-Ramanujan continued fraction
George E. Andrews · 1981
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Sums of Kloosterman sums
D. Goldfeld and P. Sarnak · 1983
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A natural representation of the Fischer-Griess Monster with the modular function J J as character
I. B. Frenkel, J. Lepowsky, and A. Meurman · 1984
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A moonshine module for the Monster
Igor B. Frenkel, James Lepowsky, and Arne Meurman · 1985
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On the Fourier coefficients of small positive powers of θ ( τ ) \theta(\tau)
M. I. Knopp · 1986
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Vertex operator algebras and the Monster
Igor Frenkel, James Lepowsky, and Arne Meurman · 1988
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On the Fourier coefficients of cusp forms having small positive weight
Marvin I. Knopp · 1989
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Classical theory of arithmetic functions
R. Sivaramakrishnan · 1989
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Modular functions and Dirichlet series in number theory
Tom M. Apostol · 1990
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Rademacher on J ( τ ) , J(\tau), Poincaré series of nonpositive weights and the Eichler cohomology
Marvin I. Knopp · 1990
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Monstrous moonshine and monstrous Lie superalgebras
Richard E. Borcherds · 1992
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Les Houches Lectures on Strings and Arithmetic
Gregory W. Moore · 2007
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Duality involving the mock theta function f ( q ) f(q)
Amanda Folsom and Ken Ono · 2008
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Ramanujan’s mock theta functions and their applications (after Zwegers and Ono-Bringmann)
Don Zagier · 2008
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Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface
Tohru Eguchi and Kazuhiro Hikami · 2009
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On weak harmonic Maass-modular grids of even integral weights
P. Guerzhoy · 2009
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A Farey tale for N=4 dyons
Sameer Murthy and Boris Pioline · 2009
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The large N limit of superconformal field theories and supergravity
Juan M. Maldacena · 1998
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Ads3 black holes and a stringy exclusion principle
Juan Maldacena and Andrew Strominger · 1998
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The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight. I
Wladimir de Azevedo Pribitkin · 1999
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The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight. II
Wladimir de Azevedo Pribitkin · 2000
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A generalization of the Goldfeld-Sarnak estimate on Selberg’s Kloosterman zeta-function
Wladimir de Azevedo Pribitkin · 2000
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Easy proofs of Riemann’s functional equation for ζ ( s ) \zeta(s) and of Lipschitz summation
Marvin Knopp and Sinai Robins · 2001
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Dyson’s ranks and Maass forms
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K 3 K3 Surfaces, N = 4 N=4 Dyons, and the Mathieu Group M 24 M_{24}
Miranda C. N. Cheng · 2010
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Mathieu Moonshine in the elliptic genus of K3
Matthias R. Gaberdiel, Stefan Hohenegger, and Roberto Volpato · 2010
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Mathieu twining characters for K3
Matthias R. Gaberdiel, Stefan Hohenegger, and Roberto Volpato · 2010
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Poincaré and analytic number theory
Emmanuel Kowalski · 2010
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Quantum gravity partition functions in three dimensions
Alexander Maloney and Edward Witten · 2010
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Zagier duality for harmonic weak Maass forms of integral weight
Bumkyu Cho and Youngju Choie · 2011
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On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine
Miranda C. N. Cheng and John F. R. Duncan · 2011
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Rademacher sums, moonshine and gravity
John F. R. Duncan and Igor B. Frenkel · 2011
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Localization and Exact Holography
Atish Dabholkar, Joao Gomes, and Sameer Murthy · 2011
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Split states, entropy enigmas, holes and halos
Frederik Denef and Gregory W. Moore · 2011
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Note on Twisted Elliptic Genus of K3 Surface
Tohru Eguchi and Kazuhiro Hikami · 2011
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Notes on the K3 Surface and the Mathieu group M 24 M_{24}
Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa · 2011
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Which AdS3 Configurations Contribute to the SCFT2 Elliptic Genus?
Sameer Murthy and Satoshi Nawata · 2011
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Coefficients of harmonic maass forms
Kathrin Bringmann and Ken Ono · 2012
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The Largest Mathieu Group and (Mock) Automorphic Forms
Miranda C. N. Cheng and John F. R. Duncan · 2012
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Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, and Jeffrey A. Harvey · 2012
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