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Let v(t) > 0 be a concave function such that´+ ∞ 1 1 tv(t) dt = +∞. If the continued fraction expansion of an irrational number 0 < θ < 1 has the coefficient a k which satisfies log 2 a k ≤ kv(k), k = 1, 2, · · · , the Julia set of e 2πiθ z + z 2 is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri  .doi:10.5186/aasfm.2018.4311 fatcat:bcuuwbr4ungwzorieukzdpbati