Mock Theta Functions

By Mock Thetafuncties. 2008

301 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d581f80f149ae6982635068529b4db2825f0ac1f

Citations in the corpus

• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues (2008, unknown): “Weakly holomorphic modular forms naturally sit in spaces of harmonic weak Maass forms (see Section 2 for definitions), more general automorphic forms which have been a source of recent interest due to their connection to Ramanujan’s mock theta functions, Borcherds products, derivatives of modular L-”
• Dyson’s ranks and Maass forms (2010, unknown): “Despite these seemingly problematic issues, Ramanujan’s mock theta functions indeed possess many striking properties, and they have been the subject of an astonishing number of important works (for example, see [5, 6, 7, 8, 12, 13, 14, 18, 19, 20, 23, 27, 28, 32, 33, 35, 36] to name a few).”
• Note on twisted elliptic genus of K3 surface (2010, unknown): “6) It is known that the above series μ(z; τ) is a typical example of a Mock theta function [25].”
• Local Analytic Classification of Q-Difference Equations (2009, unknown): “In [63], a new variable x is added (this tradition goes back to Euler) and one puts: s(α, β; q, x) := ∑”
• Zagier-type dualities and lifting maps for harmonic Maass–Jacobi forms (2010, unknown): “4 of [26] and the Poincaré series in Section 5 as explicit examples.”
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24 (2010, unknown): “It has an index 24 subgroup M23, which can be thought of as acting as permutations of 24 objects with one of them held fixed.”
• Logarithmic conformal field theory: beyond an introduction (2013, unknown): “These are familiar, but mysterious, objects in number theo ry whose modular transformations may be expressed in terms of an inte gral, the Mordell integral [134].”
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012, unknown): “It was discovered by Zwegers [119] that such forms, assuming that their poles occur only at points z ∈ Qτ + Q (i.e., at torsion points on the elliptic curve C/Zτ + Z ), have a modified theta expansion related to mock modular forms.”
• Unearthing the visions of a master: harmonic Maass forms and number theory (2008, unknown): “Indeed, recent works by the author, Andrews, Eguchi, Hikami, Kac, Lawrence, Malmendier, Mellit, Okada, Wakimoto, and Zagier [15, 18, 21, 26, 92, 120, 121, 122, 130, 131, 144, 152, 153, 211] apply this theory to: • Donaldson invariants • Gauge theory • Representation theory of Lie superalgebras • Kno”
• Eulerian series as modular forms (2007, unknown): “As usual, let f0(q), f1(q),Φ(q), and Ψ(q) denote the mock theta functions (see [2] for background and historical references)”
• Partial theta functions and mock modular forms as q-hypergeometric series (2011, unknown): “Thanks to the breakthrough of the 2002 doctoral thesis of Zwegers [28], we now finally understand how the mock theta functions fit into the theory of modular forms.”