A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
The Chowla conjecture and Landau–Siegel zeroes
Tekijät: Jaskari, Mikko; Sachpazis, Stelios
Kustantaja: Cambridge University Press (CUP)
Julkaisuvuosi: 2025
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Tietokannassa oleva lehden nimi: Mathematical Proceedings of the Cambridge Philosophical Society
Vuosikerta: 179
Numero: 1
Aloitussivu: 167
Lopetussivu: 187
ISSN: 0305-0041
eISSN: 1469-8064
DOI: https://doi.org/10.1017/S0305004125000271
Verkko-osoite: https://doi.org/10.1017/s0305004125000271
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/498491837
Let k⩾2k⩾2 be an integer and let λλ be the Liouville function. Given k non-negative distinct integers h1,…,hkh1,…,hk, the Chowla conjecture claims that ∑n⩽xλ(n+h1)⋯λ(n+hk)=o(x)∑n⩽xλ(n+h1)⋯λ(n+hk)=o(x). An unconditional answer to this conjecture is yet to be found, and in this paper, we take a conditional approach. More precisely, we establish a non-trivial bound for the sums ∑n⩽xλ(n+h1)⋯λ(n+hk)∑n⩽xλ(n+h1)⋯λ(n+hk) under the existence of a Landau–Siegel zero for x in an interval that depends on the modulus of the character whose Dirichlet series corresponds to the Landau–Siegel zero. Our work constitutes an improvement over the previous related results of Germán and Kátai, Chinis and Tao and Teräväinen.
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During the making of this work, M. Jaskari was being supported by the Academy of Finland grant no. 346307 and the University of Turku Graduate School UTUGS. S. Sachpazis acknowledges support from the Academy of Finland grant no. 333707.
