Odd order cases of the logarithmically averaged Chowla conjecture
A famous conjecture of Chowla states that the Liouville function $\lambda (n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd...
| Main Authors: | , |
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| Format: | Journal article |
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Société Arithmétique de Bordeaux
2019
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| _version_ | 1797050535764819968 |
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| author | Tao, T Teräväinen, J |
| author_facet | Tao, T Teräväinen, J |
| author_sort | Tao, T |
| collection | OXFORD |
| description | A famous conjecture of Chowla states that the Liouville function $\lambda (n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof. |
| first_indexed | 2024-03-06T18:06:35Z |
| format | Journal article |
| id | oxford-uuid:01a2f7c5-4a7a-4d39-ad6b-9a9a13f05485 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:06:35Z |
| publishDate | 2019 |
| publisher | Société Arithmétique de Bordeaux |
| record_format | dspace |
| spelling | oxford-uuid:01a2f7c5-4a7a-4d39-ad6b-9a9a13f054852022-03-26T08:36:06ZOdd order cases of the logarithmically averaged Chowla conjectureJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:01a2f7c5-4a7a-4d39-ad6b-9a9a13f05485Symplectic Elements at OxfordSociété Arithmétique de Bordeaux2019Tao, TTeräväinen, JA famous conjecture of Chowla states that the Liouville function $\lambda (n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof. |
| spellingShingle | Tao, T Teräväinen, J Odd order cases of the logarithmically averaged Chowla conjecture |
| title | Odd order cases of the logarithmically averaged Chowla conjecture |
| title_full | Odd order cases of the logarithmically averaged Chowla conjecture |
| title_fullStr | Odd order cases of the logarithmically averaged Chowla conjecture |
| title_full_unstemmed | Odd order cases of the logarithmically averaged Chowla conjecture |
| title_short | Odd order cases of the logarithmically averaged Chowla conjecture |
| title_sort | odd order cases of the logarithmically averaged chowla conjecture |
| work_keys_str_mv | AT taot oddordercasesofthelogarithmicallyaveragedchowlaconjecture AT teravainenj oddordercasesofthelogarithmicallyaveragedchowlaconjecture |