Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions
T Tao, J Teräväinen - Journal of the European Mathematical Society, 2023 - ems.press
We establish quantitative bounds on the UkŒN Gowers norms of the Möbius function and
the von Mangoldt function ƒ for all k, with error terms of the shape O.. log log N/c/. As a …
the von Mangoldt function ƒ for all k, with error terms of the shape O.. log log N/c/. As a …
On Elliott's conjecture and applications
O Klurman, AP Mangerel, J Teräväinen - arXiv preprint arXiv:2304.05344, 2023 - arxiv.org
Let $ f:\mathbb {N}\to\mathbb {D} $ be a multiplicative function. Under the merely necessary
assumption that $ f $ is non-pretentious (in the sense of Granville and Soundararajan), we …
assumption that $ f $ is non-pretentious (in the sense of Granville and Soundararajan), we …
Higher uniformity of arithmetic functions in short intervals I. All intervals
We study higher uniformity properties of the Möbius function $\mu $, the von Mangoldt
function $\Lambda $, and the divisor functions $ d_k $ on short intervals $(X, X+ H] $ with …
function $\Lambda $, and the divisor functions $ d_k $ on short intervals $(X, X+ H] $ with …
On the local Fourier uniformity problem for small sets
A Kanigowski, M Lemańczyk, FK Richter… - International …, 2024 - academic.oup.com
We consider vanishing properties of exponential sums of the Liouville function of the form
where. The case corresponds to the local-Fourier uniformity conjecture of Tao, a central …
where. The case corresponds to the local-Fourier uniformity conjecture of Tao, a central …
On arithmetic functions orthogonal to deterministic sequences
We prove the equivalence of Sarnak's conjecture on Möbius orthogonality with a
Kolmogorov type property conjectured by Veech for Furstenberg systems of the Möbius …
Kolmogorov type property conjectured by Veech for Furstenberg systems of the Möbius …
Expansion, divisibility and parity
HA Helfgott, M Radziwiłł - arXiv preprint arXiv:2103.06853, 2021 - arxiv.org
Let $\mathbf {P}\subset [H_0, H] $ be a set of primes, where $\log H_0\geq (\log
H)^{2/3+\epsilon} $. Let $\mathscr {L}=\sum_ {p\in\mathbf {P}} 1/p $. Let $ N $ be such that …
H)^{2/3+\epsilon} $. Let $\mathscr {L}=\sum_ {p\in\mathbf {P}} 1/p $. Let $ N $ be such that …
Furstenberg systems of pretentious and MRT multiplicative functions
We prove structural results for measure preserving systems, called Furstenberg systems,
naturally associated with bounded multiplicative functions. We show that for all pretentious …
naturally associated with bounded multiplicative functions. We show that for all pretentious …
Phase relations and pyramids
MN Walsh - arXiv preprint arXiv:2304.09792, 2023 - arxiv.org
arXiv:2304.09792v1 [math.NT] 19 Apr 2023 Page 1 arXiv:2304.09792v1 [math.NT] 19 Apr
2023 PHASE RELATIONS AND PYRAMIDS MIGUEL N. WALSH Abstract. We develop tools …
2023 PHASE RELATIONS AND PYRAMIDS MIGUEL N. WALSH Abstract. We develop tools …
Stability under scaling in the local phases of multiplicative functions
MN Walsh - arXiv preprint arXiv:2310.07873, 2023 - arxiv.org
We introduce a strategy to tackle some known obstructions of current approaches to the
Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for …
Fourier uniformity conjecture. Assuming GRH, we then show the conjecture holds for …
On the Hardy–Littlewood–Chowla conjecture on average
JD Lichtman, J Teräväinen - Forum of Mathematics, Sigma, 2022 - cambridge.org
On the Hardy–Littlewood–Chowla conjecture on average Page 1 Forum of Mathematics, Sigma
(2022), Vol. 10:e57 1–17 doi:10.1017/fms.2022.54 RESEARCH ARTICLE On the …
(2022), Vol. 10:e57 1–17 doi:10.1017/fms.2022.54 RESEARCH ARTICLE On the …