Some Eighth Order Mock Theta Functions

By Basil Gordon, Richard J. McIntosh. 2000

112 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/d4ac8d376cd2fc480d25e22c06241c7965d558ab

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Mock Theta Functions (2008, unknown): “Later even more exotic mock θ-functions were introduced: of sixth order (see [5]), of eighth order (see [10]) and of tenth order (see [6], [7] and [8]).”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, unknown): “…works by Andrews, Y.-S. Choi, H. Cohen, F. Dyson, Garvan, B. Gordon, Hickerson, R. McIntosh, M. Wakimoto [9] [11] [12] [14] [15] [21] [26] [27] [72] [73] [74] [75] [76] [80] [103] [104] [118] [119] [204], among numerous others, revealed many of the deeper properties of the mock theta functions.”
Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, background): “n≥0 q(−q)2n (q; q)n+1 , No(0, 1; i; q) is the eighth order mock theta function U1(q) of Gordon and McIntosh [24, 28], U1(q) = N (0, 1; i; q) = ∑”
Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions (2003, methodology): “According to this definition the functions U0(q), U1(q), V0(q), V1(q) in our paper on some eighth order mock theta functions [ 9 ] are actually first order mock theta functions, but the functions S0(q), S1(q), T0(q), T1(q) are eighth order mock theta functions.”
Hecke‐type double sums, Appell–Lerch sums, and mock theta functions, I (2012, methodology): “6) of [15], we first prove the expressions in (5.”
Second Order Mock Theta Functions (2007, background): “In our discovery [4] of the eighth order mock theta functions S0, S1, T0 and T1, Basil Gordon and I encountered the lower order mock theta functions U0, U1, V0 and V1.”
Umbral Moonshine (2012, background): “order 8 mock theta functions discussed in [59] with q-expansions”
Dyson’s ranks and Maass forms (2010, background): “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 [4], [5], [6], [7], [11], [12], [13], [17], [18], [19], [22], [26], [27], [31], [32], [34”