Lemma 2. ▇▇▇´asz-▇▇▇▇▇▇▇▇▇▇ Inequality). Let T ≥ 1, q ≥ 2. Let T ⊂ [−T, T ] be a well-spaced set, and S = T × {χ mod q}. With the same assumptions as Lemma 2.3.27, we have that (tΣ,χ)∈S F (it, χ) 2 φ(q)X + (qT )1/2 (log(2qT )) Σ| | ≪ |S| X<n 2X (n,q)=1 |an| .
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