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MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS [PDF]
Forum of Mathematics, Pi, 2013 Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM +2 more
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Singular anisotropic equations with a sign-changing perturbation
Nonlinear Analysis, 2023 We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we
Zhenhai Liu, Nikolaos S. Papageorgiou
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Singular moduli of rth Roots of modular functions
Open Mathematics, 2023 When singular moduli of Hauptmodules generate ring class fields (resp. ray class fields) of imaginary quadratic fields, using the theory of Shimura reciprocity law, we determine a necessary and sufficient condition for singular moduli of rrth roots of ...
Choi SoYoung
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A double phase equation with convection
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider a double phase problem with a gradient dependent reaction (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a nontrivial, positive, bounded solution.
Zhenhai Liu, Nikolaos Papageorgiou
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Approximation of fixed point of multivalued ρ-quasi-contractive mappings in modular function spaces [PDF]
Arab Journal of Mathematical Sciences, 2020 The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ-quasi-contractive mappings in modular function spaces.
Godwin Amechi Okeke, Safeer Hussain Khan
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Flux vacua and modularity for $\mathbb{Z}_2$ symmetric Calabi-Yau manifolds
SciPost Physics, 2023 We find continuous families of supersymmetric flux vacua in IIB Calabi-Yau compactifications for multiparameter manifolds with an appropriate $\mathbb{Z}_{2}$ symmetry.
Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern
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Fixed Points of Multivalued Maps in Modular Function Spaces
Fixed Point Theory and Applications, 2009 The purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of w-modular function and prove fixed point results for
Marwan A. Kutbi, Abdul Latif
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Ramanujan’s function k(τ)=r(τ)r2(2τ) and its modularity
Open Mathematics, 2020 We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ)k(\tau )=r(\tau ){r}^{2}(2\tau ), where r(τ)r(\tau ) is the Rogers-Ramanujan continued fraction.
Lee Yoonjin, Park Yoon Kyung
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BMS modular diaries: torus one-point function
Journal of High Energy Physics, 2020 Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions.
Arjun Bagchi +3 more
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Symmetry-resolved modular correlation functions in free fermionic theories
Journal of High Energy Physics, 2023 As a new ingredient for analyzing the fine structure of entanglement, we study the symmetry resolution of the modular flow of U(1)-invariant operators in theories endowed with a global U(1) symmetry.
Giuseppe Di Giulio, Johanna Erdmenger
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