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We prove that twisting any quasi-alternating link $L$ with no gaps in itsJones polynomial $V_L(t)$ at the crossing where it is quasi-alternatingproduces a link $L^{*}$ with no gaps in its Jones polynomial $V_{L^*}(t)$. Thisleads us to conjecture that the Jones polynomial of any prime quasi-alternatinglink, other than $(2,n)$-torus links, has no gaps. This would give a newproperty of quasi-alternating links and a simple obstruction criterion for alink to be quasi-alternating. We prove that the conjecture holds forquasi-alternating Montesinos links as well as quasi-alternating links withbraid index 3.

On The Jones Polynomial of Quasi-alternating Links