Unearthing the visions of a master: harmonic Maass forms and number theory

By Ken Ichi Ono. 2008

239 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2c03a20b9196a21c463e1e0ec97964b1945a4d59

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Partial theta functions and mock modular forms as q-hypergeometric series (2011, background): “(See for instance, the surveys of Ono [23] and Zagier [27] and the many references therein.)”
MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS (2013, background): “While the theory of weak Maass forms has led to a flood of applications in many disparate areas of mathematics (see [35, 42] and references therein), it is still not the case that we fully understand the deeper framework surrounding the contents of Ramanujan’s last letter to Hardy.”
A framework of Rogers–Ramanujan identities and their arithmetic properties (2014, background): “theory [28], conformal ﬁeld theory [10, 44, 52], group theory [32], Kac–Moody, Virasoro, vertex and double aﬃne Hecke algebras [25, 31, 50, 51, 53, 54, 55, 56], knot theory [6, 39, 40], modular forms [16, 17, 18, 19, 20, 21, 22, 63], orthogonal polynomials [7, 15, 35], statistical mechanics [4, 9], ”
Zagier-type dualities and lifting maps for harmonic Maass–Jacobi forms (2010, background): “[25] D. Zagier, Ramanujan’s mock theta functions and their applications [d’après Zwegers and Bringmann-Ono], in: Séminaire Bourbaki 60ème année, vol. 986, 2006–2007.”
Cycle integrals of the j-function and mock modular forms (2011, background): “They also motivate the study of other kinds of mock modular forms f of weight k that are paired with holomorphic modular forms g of weight 2−k in a similar way (see [38] and [50] for surveys on some of these developments).”
Umbral Moonshine (2012, background): “Descriptions of this breakthrough and some of the history of mock theta functions can be found in [55], [56] and [57].”
Eichler–Shimura theory for mock modular forms (2013, background): “1) Formula (1.16) gives an extension of the Petersson scalar product, one which works even when other “regularizations” fail.”