Built on

Dominique Foata and Marcel-P. Schützenberger, Théorie géométrique des polynômes eulériens , Lecture Notes in Mathematics, Vol. 138, Springer-Verlag, Berlin, 1970
1970
Earlier work this paper cites.
George E. Andrews, The theory of partitions , Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976, Encyclopedia of Mathematics and its Applications, Vol. 2
1976
Earlier work this paper cites.
Doron Zeilberger, The method of creative telescoping , J. Symbolic Comput. 11
1991
Earlier work this paper cites.
L. D. Faddeev, Discrete Heisenberg-Weyl group and modular group , Lett. Math. Phys. 34
1995
Earlier work this paper cites.
Kazuhiro Hikami, Hyperbolic structure arising from a knot invariant , Internat. J. Modern Phys. A 16
2001
Earlier work this paper cites.
Don Zagier, The dilogarithm function , Frontiers in number theory, physics, and geometry. II, Springer, Berlin, 2007, pp. 3–65
2007
Earlier work this paper cites.

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2013

From state integrals to q-series

Garoufalidis, Stavros, Kashaev, Rinat

Understand

It is well-known to the experts that multi-dimensional state integrals of products of Faddeev's quantum dilogarithm which arise in Quantum Topology can be written as finite sums of products of basic hypergeometric series in q=e^{2\pi i\tau} and \tilde{q}=e^{-2\pi i/\tau}.

We illustrate this fact by giving a detailed proof for a family of one-dimensional integrals which includes state-integral invariants of 4_1 and 5_2 knots.

Built on

Dominique Foata and Marcel-P. Schützenberger, Théorie géométrique des polynômes eulériens , Lecture Notes in Mathematics, Vol. 138, Springer-Verlag, Berlin, 1970
1970
Earlier work this paper cites.
George E. Andrews, The theory of partitions , Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976, Encyclopedia of Mathematics and its Applications, Vol. 2
1976
Earlier work this paper cites.
Doron Zeilberger, The method of creative telescoping , J. Symbolic Comput. 11
1991
Earlier work this paper cites.
L. D. Faddeev, Discrete Heisenberg-Weyl group and modular group , Lett. Math. Phys. 34
1995
Earlier work this paper cites.
Kazuhiro Hikami, Hyperbolic structure arising from a knot invariant , Internat. J. Modern Phys. A 16
2001
Earlier work this paper cites.
Don Zagier, The dilogarithm function , Frontiers in number theory, physics, and geometry. II, Springer, Berlin, 2007, pp. 3–65
2007
Earlier work this paper cites.

Similar

Tudor Dimofte, Sergei Gukov, Jonatan Lenells, and Don Zagier, Exact results for perturbative Chern-Simons theory with complex gauge group , Commun. Number Theory Phys. 3
2009
Cited alongside, same era.
Masha Vlasenko, Computation of an asymptotics related to nahm’s conjecture , Preprint 2010
2010
Cited alongside, same era.
Jørgen E. Andersen and Rinat M. Kashaev, A TQFT from quantum Teichmüller theory , arXiv:1109.6295
Original
2011
Cited alongside, same era.
Tudor Dimofte, Davide Gaiotto, and Sergei Gukov, 3-manifolds and 3d indices , arXiv:1112.5179
Original
2011
Cited alongside, same era.
by same author, Gauge theories labelled by three-manifolds , arXiv:1108.4389
Original
2011

Then

Fernando Rodriguez-Villegas, A refinement of the A A -polynomial of quivers , Preprint 2011
2011
Later among the works it cites.
Masha Vlasenko and Sander Zwegers, Nahm’s conjecture: asymptotic computations and counterexamples , Commun. Number Theory Phys. 5
2011
Later among the works it cites.
Stavros Garoufalidis, The 3D index of an ideal triangulation and angle structures , arXiv:1208.1663
Original
2012
Later among the works it cites.
Rinat M. Kashaev, Feng Luo, and Grigory Vartanov, A TQFT of turaev-viro type on shaped triangulations , 2012, arXiv:1210.8393
Original
2012
Later among the works it cites.
Stavros Garoufalidis, Craig D. Hodgson, Hyam Rubinstein, and Henry Segerman, 1 1 -efficient triangulations and the index of a cusped hyperbolic 3-manifold , arXiv:1303.5278
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

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Cited alongside, same era.

Maxim Kontsevich and Yan Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants , Commun. Number Theory Phys. 5

2011

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N.J.A. Sloane, The online encyclopedia of integer sequences , http://oeis.org

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2013

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Stavros Garoufalidis and Don Zagier, Empirical relations between q q -series and kashaev’s invariant of knots , Preprint 2013

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