Results 21 to 30 of about 808 (120)

New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
doaj   +1 more source

K-RUN OVERPARTITIONS AND MOCK THETA FUNCTIONS [PDF]

The Quarterly Journal of Mathematics, 2012
11 pages, 1 ...
Bringmann, Kathrin, Holroyd, A. E., Mahlburg, K., Vlasenko, M.   +3 more
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Mock Theta Functions

, 2008
In this Ph.D. thesis, written under the direction of D.B. Zagier and R.W. Bruggeman, we study the mock theta functions, that were introduced by Ramanujan. We show how they can be interpreted in the theory of (real-analytic) modular forms. In Chapter 1 we give results for Lerch sums (also called Appell functions, or generalized Lambert series).
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Three-manifold quantum invariants and mock theta functions [PDF]

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019
Mock modular forms have found applications in numerous branches of mathematical sciences since they were first introduced by Ramanujan nearly a century ago. In this proceeding, we highlight a new area where mock modular forms start to play an important role, namely the study of three-manifold invariants.
Cheng, M.C.N., Ferrari, F., Sgroi, G.
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q-hypergeometric double sums as mock theta functions [PDF]

Pacific Journal of Mathematics, 2013
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.
Lovejoy, Jeremy, Osburn, Robert
openaire   +5 more sources

Orientation reversal and the Chern-Simons natural boundary

Journal of High Energy Physics
We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics.
Griffen Adams, Ovidiu Costin, Gerald V. Dunne, Sergei Gukov, Oğuz Öner   +4 more
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Sixth order mock theta functions

Advances in Mathematics, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berndt, B.C., Chan, S.H.
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Black hole quantum mechanics and generalized error functions

Journal of High Energy Physics
In Type II Calabi-Yau string compactifications, S-duality predicts that suitable generating series of BPS indices counting microstates of D4-D2-D0 black holes are in general mock modular forms of higher depth.
Boris Pioline, Rishi Raj
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Mock Theta Functions and Related Combinatorics

In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious $q$-hypergeometric series introduced by Ramanujan in his last letter to Hardy in 1920, which we now know to be important examples of mock modular forms.
Ballantine, Cristina, Burson, Hannah E., Folsom, Amanda, Hsu, Chi-Yun, Negrini, Isabella, Wen, Boya   +5 more
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A Mock Theta Function of Second Order [PDF]

International Journal of Mathematics and Mathematical Sciences, 2009
We consider the second‐order mock theta function 𝒟5 (q), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold. We give their bilateral form, and show that it is the same as bilateral third‐order mock theta function of Ramanujan. We also show that the mock theta function 𝒟5 (q) outside the unit circle is a
openaire   +2 more sources