Year: 2026
Type: preprint
Abstract: We prove a Bombieri-Vinogradov type theorem for exponential sums over products of $k$ primes. As an application, we show the lower bound $$\sup_{n\le x} \left|\sum_{m\le n} 1_{Ω(m) = k} e(αm)\right| \gg x^{1/6 - \varepsilon}$$ for $2\le k\le (2-\varepsilon)\log\log x$ and $α\in\mathbb{R},$ where we noted $e(β) := e^{2iπβ}.$
Source: arXiv (Cornell University)
Author: Bazin, Péa
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169530923