Quantum modular forms

By Don Zagier. 2010

227 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0b9bb322fbfbd4033600ed23a3b558192020573

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Period functions and cotangent sums (2011, background): “” This is nearly an example of what Zagier calls a “quantum modular form” [Zagier 2010].”
Chern-Simons theory and S-duality (2011, background): “Closer to the current developments is a series of observations [8, 9] that analytically continued partition function on hyperbolic 3-manifolds exhibits even more delicate modular behavior which, in the context of state integral models for Chern-Simons theory [10, 11], can be traced to the correspond”
MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS (2013, background): “Here, we prove Theorem 1.3 after first proving a lemma about the convergence of relevant q-hypergeometric series at roots of unity, and after recalling important results of Lawrence and Zagier [31] and Bringmann and the second two authors [17].”
A q-microscope for supercongruences (2018, background): “We remark that asymptotic behavior of q-series at roots of unity attracts a lot of attention in recent studies of mock theta functions and so-called quantum modular forms; we limit our citations about related notion and results to [4, 33].”
A Reciprocity Formula for a Cotangent Sum (2013, background): “We remark that c(x) is (nearly) an example of what Zagier calls a “quantum modular form” (see [11]).”
On the asymptotic expansion of the Kashaev invariant of the $5_2$ knot (2016, background): “Furthermore, it is conjectured [11] (see also [3, 12, 46]) from the viewpoint of the SL(2,C) Chern-Simons theory that the asymptotic expansion of JN(K; e √ −1/k)”
Exact results for perturbative Chern-Simons theory with complex gauge group. (2009, background): “The arithmeticity conjecture discussed here is a part of a richer structure: the quantum GC invariants are only the special case x = 0 of a collection of functions indexed by rational numbers x which each have asymptotic expansions in ~ satisfying the arithmeticity conjecture and which have a certai”
Torus knots and quantum modular forms (2014, background): “Introduction and statement of results Several years ago, Zagier introduced quantum modular forms [30].”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “An alternative hint of S-duality (in fact, of modularity) in certain colored Jones polynomials was also found in [84].”