English
Higher order uniformity of the Möbius function
Virtualconference
Auteurs : Matomäki, Kaisa (Auteur de la conférence)
CIRM (Editeur )
11N25 - Distribution of integers with specified multiplicative constraints
11N64 - Other results on the distribution of values or the characterization of arithmetic functions
11B30 - Arithmetic combinatorics; higher degree uniformity
CIRM (Editeur )
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Résumé :
The Liouville function $\lambda(n)$ takes the value +1 or -1 depending on whether $n$ has an even or an odd number of prime factors. The Liouville function is closely related to the characteristic function of the primes and is believed to behave more-or-less randomly.
I will discuss my very recent work with Radziwill, Tao, Teräväinen, and Ziegler, where we show that, in almost all intervals of length $X^{\varepsilon}$, the Liouville function does not correlate with polynomial phases or more generally with nilsequences.
I will also discuss applications to superpolynomial number of sign patterns for the Liouville sequence and to a new averaged version of Chowla's conjecture.
Mots-Clés : Liouville function; higher order uniformity; Chowla's conjecture
Codes MSC : I will discuss my very recent work with Radziwill, Tao, Teräväinen, and Ziegler, where we show that, in almost all intervals of length $X^{\varepsilon}$, the Liouville function does not correlate with polynomial phases or more generally with nilsequences.
I will also discuss applications to superpolynomial number of sign patterns for the Liouville sequence and to a new averaged version of Chowla's conjecture.
Mots-Clés : Liouville function; higher order uniformity; Chowla's conjecture
11N25 - Distribution of integers with specified multiplicative constraints
11N64 - Other results on the distribution of values or the characterization of arithmetic functions
11B30 - Arithmetic combinatorics; higher degree uniformity
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 29/09/2020 Date de Captation : 10/09/2020 Sous Collection : Research talks Catégorie arXiv : Number Theory Domaine(s) : Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:34:37 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-09-10_Matomaki.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Additive Combinatorics / Combinatoire additiveOrganisateurs de la Rencontre : Balandraud, Eric ; Dousse, Jehanne ; Girard, Benjamin ; Schmid, Wolfgang ; Tringali, Salvatore Dates : 07/09/2020 - 11/09/2020 Année de la rencontre : 2020 URL de la Rencontre : https://conferences.cirm-math.fr/2228.html
Données de citation
DOI : 10.24350/CIRM.V.19653803Citer cette vidéo: Matomäki, Kaisa (2020). Higher order uniformity of the Möbius function. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19653803 URI : http://dx.doi.org/10.24350/CIRM.V.19653803 |
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Bibliographie
- MATOMÄKI, Kaisa, RADZIWIŁŁ, Maksym, TAO, Terence, et al. Higher uniformity of bounded multiplicative functions in short intervals on average. arXiv preprint arXiv:2007.15644, 2020. - https://arxiv.org/abs/2007.15644
