PreprintCC BY 4.0arXiv
A Bombieri-Vinogradov theorem for exponential sums over products of k primes
Abstract
We prove a Bombieri-Vinogradov type theorem for exponential sums over products of k primes. As an application, we show the lower bound supn≤ x |∑m≤ n 1Ω(m) = k e(αm)| ≫ x1/6 − ε for 2≤ k≤ (2−ε)loglog x and α∈ℝ, where we noted e(β) := e2iπβ.
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BibTeX
@misc{bazin2026bombierivinogradov,
title = {{A Bombieri-Vinogradov theorem for exponential sums over products of k primes}},
author = {Péa Bazin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15137},
eprint = {2607.15137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15137},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bombieri-Vinogradov theorem for exponential sums over products of k primes
AU - Péa Bazin
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2607.15137
UR - https://arxiv.org/abs/2607.15137
AB - 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.
ER -