Results 1 to 10 of about 293 (45)
Mock theta functions and Appell–Lerch sums [PDF]
Journal of Inequalities and Applications, 2018 Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
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Dyson’s ranks and Appell–Lerch sums [PDF]
Mathematische Annalen, 2016 substantially ...
Hickerson, Dean, Mortenson, Eric
core +16 more sources
Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I [PDF]
Proceedings of the London Mathematical Society, 2014 By developing a connection between partial theta functions and Appell-Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell-Lerch sums and theta functions. Not only does our formula prove classical Hecke-type double sum identities such as those found in work Kac and Peterson on affine Lie Algebras and Hecke ...
Hickerson, Dean R., Mortenson, Eric T.
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On the dual nature of partial theta functions and Appell–Lerch sums
Advances in Mathematics, 2014 To be published in Advances in ...
Andrews +28 more
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TWO CONGRUENCES FOR APPELL–LERCH SUMS
International Journal of Number Theory, 2012 Two congruences are proved for an infinite family of Appell–Lerch sums. As corollaries, special cases imply congruences for some of the mock theta functions of order two, six and eight.
Chan, Song Heng, Mao, Renrong
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Bilateral series in terms of mixed mock modular forms
Journal of Inequalities and Applications, 2016 The number of strongly unimodal sequences of weight n is denoted by u ∗ ( n ) $u^{*}(n)$ . The generating functions for { u ∗ ( n ) } n = 1 ∞ $\{u^{*}(n)\}_{n=1}^{\infty}$ are U ∗ ( q ) = ∑ n = 1 ∞ u ∗ ( n ) q n $U^{*}(q)=\sum_{n=1}^{\infty}u^{*}(n)q^{n}$
Bin Chen, Haigang Zhou
doaj +1 more source
q-hypergeometric double sums as mock theta functions [PDF]
, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
core +3 more sources
A heuristic guide to evaluating triple-sums
, 2020 Using a heuristic that relates Appell--Lerch functions to divergent partial theta functions one can expand Hecke-type double-sums in terms of Appell--Lerch functions.
Mortenson, Eric T.
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Asymptotic formulae for partition ranks [PDF]
, 2014 Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F.
Dousse, Jehanne, Mertens, Michael H.
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On recursions for coefficients of mock theta functions [PDF]
, 2015 We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions.
Chan, Song Heng +2 more
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