Texture zeros of quark mass matrices at fixed point τ = ω in modular flavor symmetry

We study systematically derivation of the specific texture zeros, that is the nearest neighbor interaction (NNI) form of the quark mass matrices at the fixed point τ = ω in modular flavor symmetric models. We present models that the NNI forms of the quark mass matrices are simply realized at the fixed point τ = ω in the A${}_4$ modular flavor symmetry by taking account multi-Higgs fields. Such texture zero structure originates from the ST charge of the residual symmetry Z${}_3$ of SL(2, Z). The NNI form can be realized at the fixed point τ = ω in A${}_4$ and S${}_4$ modular flavor models with two pairs of Higgs fields when we assign properly modular weights to Yukawa couplings and A${}_4$ and S${}_4$ representations to three generations of quarks. We need four pairs of Higgs fields to realize the NNI form in A${}_5$ modular flavor models.