Abstract
In the theory of harmonic Maaß forms and mock modular forms, mock theta functions are distinguished examples which arose from q-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms, which we call higher depth mock theta functions, and develop q-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a q-hypergeometric series.
Acknowledgements
We would like to thank Jeremy Lovejoy for insightful discussions on partition-theoretic aspects of this paper. In addition, we would like to thank Kathrin Bringmann for useful comments on an earlier version of this paper. We also thank the referee for many helpful suggestions.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Higher depth mock theta functions and q-hypergeometric series
- Topological and algebraic properties of universal groups for right-angled buildings
- On the socles of characteristically inert subgroups of Abelian p-groups
- Priestley duality for MV-algebras and beyond
- The cardinality of μM,D‐orthogonal exponentials for the planar four digits
- Associated prime ideals of equivariant coinvariant algebras, Steenrod operations, and Krull’s Going Down Theorem
- Ordered fields dense in their real closure and definable convex valuations
- Third Hankel determinants for two classes of analytic functions with real coefficients
- A common range problem for model spaces
- Generalized Ricci flow on nilpotent Lie groups
- Endpoint estimates for a trilinear pseudo-differential operator with flag symbols
- The role of the algebraic structure in Wold-type decomposition
- Incidences between Euclidean spaces over finite fields
- Cancellation in algebraic twisted sums on GL_m
Articles in the same Issue
- Frontmatter
- Higher depth mock theta functions and q-hypergeometric series
- Topological and algebraic properties of universal groups for right-angled buildings
- On the socles of characteristically inert subgroups of Abelian p-groups
- Priestley duality for MV-algebras and beyond
- The cardinality of μM,D‐orthogonal exponentials for the planar four digits
- Associated prime ideals of equivariant coinvariant algebras, Steenrod operations, and Krull’s Going Down Theorem
- Ordered fields dense in their real closure and definable convex valuations
- Third Hankel determinants for two classes of analytic functions with real coefficients
- A common range problem for model spaces
- Generalized Ricci flow on nilpotent Lie groups
- Endpoint estimates for a trilinear pseudo-differential operator with flag symbols
- The role of the algebraic structure in Wold-type decomposition
- Incidences between Euclidean spaces over finite fields
- Cancellation in algebraic twisted sums on GL_m