A Bombieri-Vinogradov theorem for exponential sums over products of k primes

2026/07/16 by Pierre-Alexandre Bazin
#math.NT

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Abstract

We prove a Bombieri-Vinogradov type theorem for exponential sums over products of k primes. As an application, we show the lower bound sup_{n≤ x} |∑_{m≤ n} 1_{Ω(m) = k} e(αm)| ≫ x^{1/6 - ε} for 2≤ k≤ (2-ε)loglog x and α∈ℝ, where we noted e(β) := e^2iπβ.

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