On vector-valued modular forms and their Fourier coefficients
Marvin I. Knopp,Geoffrey Mason +1 more
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This article is published in Acta Arithmetica.The article was published on 2003-01-01 and is currently open access. It has received 64 citations till now. The article focuses on the topics: Eisenstein series & Hecke operator.read more
Citations
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W-Algebra W(2, 2) and the Vertex Operator Algebra {L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}
Wei Zhang,Chongying Dong +1 more
TL;DR: In this paper, it was shown that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex algebra associated to an irreducible highest weight W(2, 2)- module or a tensor product of two simple Virasoro vertex operator algebras.
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Rational Vertex Operator Algebras and the Effective Central Charge
Chongying Dong,Geoffrey Mason +1 more
TL;DR: In this paper, it was shown that the Lie algebra of weight one states in a rational vertex operator algebra is reductive, and that its Lie rank is bounded above by the effective central charge.
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Congruence property in conformal field theory
TL;DR: The congruence subgroup property of the modular representations associated to any modular tensor category was established in this paper, and the order of the anomaly for those modular categories satisfying some integrality conditions was determined.
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Vector-valued modular forms and linear differential operators
TL;DR: In this article, the authors consider holomorphic vector-valued modular forms F of integral weight k on the full modular group Γ = SL(2, ℤ) corresponding to representations of Γ of arbitrary finite dimension p. Assuming that the component functions of F are linearly independent, the inequality k ≥ 1 - p always holds, and that equality holds only in the trivial case when p = 1 and k = 0.
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Congruence Property In Conformal Field Theory
TL;DR: The congruence subgroup property of the modular representations associated to any modular tensor category is established in this paper, and the order of the anomaly for those modular categories satisfying some integrality conditions is determined.
References
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Modular invariance of characters of vertex operator algebras
TL;DR: In this article, it was shown that the characters of the integrable highest weight modules of affine Lie algebras and the minimal series of the Virasoro algebra give rise to conformal field theories.
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Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine
TL;DR: In this article, the authors provide a mathematically rigorous foundation for rational vertex operator algebras and their automorphisms in the theory of rational orbifold models in conformal field theory.
Book
Modular Forms and Functions
TL;DR: In this article, the authors present a general characterization of modular forms, including groups of matrices and bilinear mappings, groups of level 2 and sums of squares, hecke operators and congruence groups.
Book
Modular functions in analytic number theory
TL;DR: Knopp as discussed by the authors presents an introduction to modular functions in number theory by concentrating on two modular functions, and their applications to two number-theoretic functions, $p(n)$ and $r_s(n).
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Generalized modular forms
Marvin I. Knopp,Geoffrey Mason +1 more
TL;DR: In this paper, it was shown that the q-series of necessity behave like modular forms in every respect, with the important exception that the multiplier system need not be of absolute value one.