A Generalized Jacobi Theta Function and Quasimodular Forms

Kaneko, Masanobu; Zagier, Don

doi:10.1007/978-1-4612-4264-2_6

Cited by 272 publications

(397 citation statements)

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“…A qualitative conclusion which may be drawn is that the z-coefficients of (5. the quasimodularity (5.4) generalizes the quasimodularity of generating functions for simply branched coverings of the torus studied in [4], [22].…”

Section: The Gromov-witten Theory Of An Elliptic Curvementioning

confidence: 83%

Gromov–Witten theory, Hurwitz theory, and completed cycles

2006

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Section: The Gromov-witten Theory Of An Elliptic Curvementioning

confidence: 83%

Gromov–Witten theory, Hurwitz theory, and completed cycles

2006

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“…Kaneko and Zagier, [21], refer to the algebra generated by ǫ 1 , ǫ 2 and ǫ 3 as the algebra of quasi-modular forms.…”

Section: Temperature Inversionmentioning

confidence: 99%

Elliptic aspects of statistical mechanics on spheres

Dowker

Kirsten

2008

Journal of Mathematical Physics

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Our earlier results on the temperature inversion properties and the ellipticisation of the finite temperature internal energy on odd spheres are extended to orbifold factors of odd spheres and then to other thermodynamic quantities, in particular to the specific heat. The behaviour under modular transformations is facilitated by the introduction of a modular covariant derivative and it is shown that the specific heat on any odd sphere can be expressed in terms of just three functions. It is also shown that the free energy on the circle can be written elliptically.

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“…A rigorous proof was subsequently presented in [49,50] directly from the equivalent free fermion representation of the partition function [52]. Another proof, based on similar considerations, is presented in Appendix B (see also [53]).…”

Section: Gross-taylor Series On the Torusmentioning

confidence: 99%

Instantons, fluxons, and open gauge string theory

Seminara¹,

Szabo²

2005

Advances in Theoretical and Mathematical Physics

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Abstract:We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.

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A Generalized Jacobi Theta Function and Quasimodular Forms

Cited by 272 publications

References 1 publication

Gromov–Witten theory, Hurwitz theory, and completed cycles

Gromov–Witten theory, Hurwitz theory, and completed cycles

Elliptic aspects of statistical mechanics on spheres

Instantons, fluxons, and open gauge string theory

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