# Siegel Zeros and Sarnak's Conjecture

@inproceedings{Chinis2021SiegelZA, title={Siegel Zeros and Sarnak's Conjecture}, author={Jake Chinis}, year={2021} }

Abstract. Assuming the existence of Siegel zeros, we prove that there exists an increasing sequence of positive integers for which Chowla’s Conjecture on k-point correlations of the Liouville function holds. This extends work of Germán and Kátai, where they studied the case k = 2 under identical hypotheses. An immediate corollary, which follows from a well-known argument due to Sarnak, is that Sarnak’s Conjecture on Möbius disjointness holds. More precisely, assuming the existence of Siegel…

## 3 Citations

On arithmetic functions orthogonal to deterministic sequences

- Mathematics
- 2021

Abstract We prove Veech’s conjecture on the equivalence of Sarnak’s conjecture on Möbius orthogonality with a Kolmogorov type property of Furstenberg systems of the Möbius function. This yields a…

On the Hardy-Littlewood-Chowla conjecture on average

- Mathematics
- 2021

There has been recent interest in a hybrid form of the celebrated conjectures of Hardy–Littlewood and of Chowla. We prove that for any k, ` ≥ 1 and distinct integers h2, . . . , hk, a1, . . . , a`,…

Quantitative bounds for Gowers uniformity of the M\"obius and von Mangoldt functions

- Mathematics
- 2021

We establish quantitative bounds on the U[N ] Gowers norms of the Möbius function μ and the von Mangoldt function Λ for all k, with error terms of shapeO((log logN)−c). As a consequence, we obtain…

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