منابع مشابه
The Bailey Transform and False Theta Functions
An empirical exploration of five of Ramanujan’s intriguing false theta function identities leads to unexpected instances of Bailey’s transform which, in turn, lead to many new identities for both false and partial theta functions.
متن کاملMock (false) Theta Functions as Quantum Invariants
We establish a correspondence between the SU(2) Witten–Reshetikhin–Turaev invariant for the Seifert manifold M(p1, p2, p3) and Ramanujan’s mock theta functions.
متن کاملRamanujan’s Partial Theta Series and Parity in Partitions
A partial theta series identity from Ramanujan’s lost notebook has a connection with some parity problems in partitions studied by Andrews in [3], where 15 open problems are listed. In this paper, the partial theta series identity of Ramanujan is revisited and answers to Questions 9 and 10 of Andrews are provided.
متن کاملFALSE, PARTIAL, AND MOCK JACOBI THETA FUNCTIONS AS q-HYPERGEOMETRIC SERIES
to add 1. Curious q-series Identities Since Rogers [32] introduced the false theta functions, they have played a curious role in the theory of partitions (see for instance [1, 2, 12]). Andrews [3] defined a false theta function as any series of the shape ∑ n∈Z(±1)q 2+`n that has different signs for the nonzero terms. For example, Rogers proved (1.1) ∑ j≥0 q j(3j+1) 2 − ∑ j≤−1 q j(3j+1) 2 = ∑ j≥...
متن کاملPartitions with short sequences and mock theta functions.
P. A. MacMahon was the first to examine integer partitions in which consecutive integers were not allowed as parts. Such partitions may be described as having sequences of length 1. Recently it was shown that partitions containing no sequences of consecutive integers of length k are of interest in seemingly unrelated problems concerning threshold growth models. The object now is to develop the ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1972
ISSN: 0035-7596
DOI: 10.1216/rmj-1972-2-1-49