Abstract
Let f : ℕ → ℂ be a bounded multiplicative function. Let a be a fixed non-zero integer (say a = 1). Then f is well distributed on the progression n ≡ a (mod q) ⊂ {1,…, X}, for almost all primes q ∈ [Q, 2Q], for Q as large as X1/2+1/78−o(1).
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