• Corpus ID: 238856924

A conjecture of Zagier and the value distribution of quantum modular forms

  title={A conjecture of Zagier and the value distribution of quantum modular forms},
  author={Christoph Aistleitner and Bence Borda},
In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modular group on their argument. More precisely, when JK,0 denotes the colored Jones polynomial of a knot K, Zagier’s modularity conjecture describes the asymptotics of the quotient JK,0(e )/JK,0(e ) as x→ ∞ along rationals with bounded denominators, where γ ∈ SL(2,Z). This problem is most accessible for the figure-eight… 
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