In a joint work with Qingtao Chen,we conjecture that at the root of unity exp(2πi/r)instead of the usually considered root exp(πi/r),the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic 3-manifold grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold.This reveals a different asymptotic behavior of the relevant quantum invariants than that of Wittens invariants(that grow polynomially by the Asymptotic Expansion Conjecture),which may indicate a different geometric interpretation of the Reshetikhin-Turaev invariants than the SU(2)Chern-Simons gauge theory.