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Osburn, Robert
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Osburn, Robert
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Osburn, Robert
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Now showing 1 - 5 of 5
- PublicationMixed Mock Modular Q-seriesMixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common than mock theta functions. In this survey we discuss some of the ways such series arise.
101 - PublicationMock theta double sumsWe prove a general result on Bailey pairs and show that two Bailey pairs of Bringmann and Kane are special cases. We also show how to use a change of base formula to pass from the pairs of Bringmann and Kane to pairs used by Andrews in his study of Ramanujan's seventh order mock theta functions. We derive several more Bailey pairs of a similar type and use these to construct a number of new q-hypergeometric double sums which are mock theta functions. Finally, we prove identities between some of these mock theta double sums and classical mock theta functions.
148Scopus© Citations 12 - PublicationReal quadratic double sumsIn 1988, Andrews, Dyson and Hickerson initiated the study of q-hypergeometric series whose coefficients are dictated by the arithmetic in real quadratic fields. In this paper, we provide a dozen q-hypergeometric double sums which are generating functions for the number of ideals of a given norm in rings of integers of real quadratic fields and prove some related identities.
216Scopus© Citations 7 - PublicationRogers-Ramanujan type identities for alternating knotsWe highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers–Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Lê and Zagier.
276Scopus© Citations 13 - PublicationThe Bailey chain and mock theta functionsStandard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain classical mock theta functions.
358Scopus© Citations 20