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Perspectives on mock modular forms (Q518104)

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scientific article; zbMATH DE number 6697574

Language	Label	Description	Also known as
English	Perspectives on mock modular forms	scientific article; zbMATH DE number 6697574

Statements

scholarly article

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Perspectives on mock modular forms (English)

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Journal of Number Theory

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publication date

28 March 2017

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zbMATH Keywords

mock modular forms

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mock theta functions

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harmonic Maass forms

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modular forms

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theta functions

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Maass forms

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\(q\)-series

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describes a project that uses

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MaRDI profile type

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full work available at URL

https://doi.org/10.1016/j.jnt.2017.02.001

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\(\ell \)-adic properties of smallest parts functions

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Rank generating functions as weakly holomorphic modular forms

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Twisted traces of CM values of weak Maass forms

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Weierstrass mock modular forms and elliptic curves

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Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes

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Periods of the <i>j</i> -function along infinite geodesics and mock modular forms

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An Introduction to Ramanujan's "lost" Notebook

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Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks

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The Selected Works of George E Andrews

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Partitions associated with the Ramanujan/Watson mock theta functions \(\omega(q)\), \(\nu(q)\) and \(\phi(q)\)

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Partitions and indefinite quadratic forms.

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Modularity of the concave composition generating function

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Some Properties of Partitions

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Monstrous moonshine and monstrous Lie superalgebras

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Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products

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What is moonshine

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Negative index Jacobi forms and quantum modular forms

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Almost harmonic Maass forms and Kac-Wakimoto characters

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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications

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Unimodal sequences and ``strange'' functions: a family of quantum modular forms

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On cycle integrals of weakly holomorphic modular forms

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\(k\)-run overpartitions and mock theta functions

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Overpartitions and class numbers of binary quadratic forms

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An extension of the Hardy-Ramanujan circle method and applications to partitions without sequences

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Taylor coefficients of mock-Jacobi forms and moments of partition statistics

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From sheaves on \(\mathbb{P}^2\) to a generalization of the Rademacher expansion

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The \(f(q)\) mock theta function conjecture and partition ranks

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Dyson's ranks and Maass forms

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Eulerian series as modular forms

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Radial limits of mock theta functions

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On two geometric theta lifts

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Traces of CM values of modular functions

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Regularized theta liftings and periods of modular functions

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Heegner divisors, \(L\)-functions and harmonic weak Maass forms

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Computation of Harmonic Weak Maass Forms

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\(K3\) surfaces, \({\mathcal N}=4\) dyons and the Mathieu group \(M_{24}\)

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Umbral moonshine

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Umbral moonshine and the Niemeier lattices

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Umbral moonshine and \(K3\) surfaces

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Shimura lifting on weak Maass forms

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Monstrous Moonshine

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Modular equations and the genus zero property of moonshine functions

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Almost a century of answering the question: what is a mock theta function?

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Rational period functions and cycle integrals

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Cycle integrals of the \(j\)-function and mock modular forms

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Real Quadratic Analogs of Traces of Singular Moduli

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Integral traces of singular values of weak Maass forms

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Harmonic Maass forms of weight 1

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Proof of the umbral moonshine conjecture

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Notes on the K3 Surface and the Mathieu Group<i>M</i><sub>24</sub>

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The theory of Jacobi forms

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Mock theta functions and quantum modular forms

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A natural representation of the Fischer-Griess Monster with the modular function <i>J</i> as character

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Mathieu moonshine in the elliptic genus of K3

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Mathieu twining characters for \(K3\)

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MONSTROUS MOONSHINE: THE FIRST TWENTY-FIVE YEARS

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Much ado about Mathieu

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THE COEFFICIENTS OF THE ω(q) MOCK THETA FUNCTION

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Higher order spt-functions

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Automorphic Forms and L-Functions for the Group<i>GL</i>(<i>n</i>, R)

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Modular transformations of Ramanujan's fifth and seventh order mock theta functions

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A Survey of Classical Mock Theta Functions

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Jacobi forms and the structure of Donaldson invariants for 4-manifolds with \(b_+=1\)

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A construction of <i>F</i> <sub>1</sub> as automorphisms of a 196,883-dimensional algebra

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The friendly giant

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SU(2)-Donaldson invariants of the complex projective plane

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A proof of the Thompson moonshine conjecture

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Ramanujan’s mock theta functions

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Heegner points and derivatives of \(L\)-series. II

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Heegner points and derivatives of \(L\)-series

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On Zagier's adele

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A mixed mock modular solution of the Kaneko-Zagier equation

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Congruences for Taylor expansions of quantum modular forms

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A proof of the mock theta conjectures

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Hecke-type double sums, Appell-Lerch sums, and mock theta functions. I.

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Torus knots and quantum modular forms

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Automorphic forms with singularities on the hyperbolic space

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Holomorphic projections and Ramanujan’s mock theta functions

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Radial limits of the universal mock theta function 𝑔₃

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Mock Jacobi forms in basic hypergeometric series

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Borcherds products associated with certain Thompson series

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The Bailey chain and mock theta functions

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Mixed mock modular q-series

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\(q\)-hypergeometric double sums as mock theta functions

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Donaldson invariants of \(\mathbb CP^1 \times \mathbb CP^1\) and mock theta functions

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Moonshine for \(M_{24}\) and Donaldson invariants of \(\mathbb{C} \text{P}^2\)

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SO(3)-Donaldson invariants of \(\mathbb CP^{2}\) and mock theta functions

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The asymptotic distribution of traces of cycle integrals of the \(j\)-function

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Eichler-Selberg type identities for mixed mock modular forms

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Integration over the \(u\)-plane in Donaldson theory

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The Mathematical Legacy of Srinivasa Ramanujan

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Vector-valued modular forms and the mock theta conjectures

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Definite quadratische Formen der Dimension 24 und Diskriminante 1

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On the Fourier coefficients of meromorphic Jacobi forms

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Classical and Umbral Moonshine: Connections and $p$-adic Properties

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Second-quantized Mathieu moonshine

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On Ramanujan’s definition of mock theta function

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A ``strange'' vector-valued quantum modular form

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On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)

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Electric-magnetic duality, monopole condensation, and confinement in \(N=2\) supersymmetric Yang-Mills theory

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Some Numerology between the Fischer-Griess Monster and the Elliptic Modular Function

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A strong coupling test of \(S\)-duality

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On certain explicit congruences for mock theta functions

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The Final Problem : An Account of the Mock Theta Functions

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Elliptic functions according to Eisenstein and Kronecker.

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On \(S\)-duality in abelian gauge theory

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The Betti numbers of the moduli space of stable sheaves of rank2 on P2.

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Elliptic Modular Forms and Their Applications

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On three theorems of Folsom, Ono and Rhoades

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Mock \(\vartheta\)-functions and real analytic modular forms.

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Mock Maass theta functions

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On the Fourier coefficients of positive index meromorphic Jacobi forms

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1016/J.JNT.2017.02.001

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Sitelinks

Mathematics(1 entry)

mardi Publication:518104

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