Transcendence of Hecke-Mahler series
We prove transcendence of the Hecke-Mahler series ∑∞n=0f(⌊nθ+α⌋)β−n, where f(x)∈Z[x] is a non-constant polynomial α is a real number, θ is an irrational real number, and β is an algebraic number such that |β|>1.
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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London Mathematical Society
2025
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| _version_ | 1824459102427807744 |
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| author | Luca, F Ouaknine, J Worrell, JB |
| author_facet | Luca, F Ouaknine, J Worrell, JB |
| author_sort | Luca, F |
| collection | OXFORD |
| description | We prove transcendence of the Hecke-Mahler series ∑∞n=0f(⌊nθ+α⌋)β−n, where f(x)∈Z[x] is a non-constant polynomial α is a real number, θ is an irrational real number, and β is an algebraic number such that |β|>1. |
| first_indexed | 2025-02-19T04:36:27Z |
| format | Journal article |
| id | oxford-uuid:7d94b8fe-ad5e-456e-9838-69aca1a454d6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:36:27Z |
| publishDate | 2025 |
| publisher | London Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:7d94b8fe-ad5e-456e-9838-69aca1a454d62025-02-04T16:17:12ZTranscendence of Hecke-Mahler seriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7d94b8fe-ad5e-456e-9838-69aca1a454d6EnglishSymplectic ElementsLondon Mathematical Society2025Luca, FOuaknine, JWorrell, JBWe prove transcendence of the Hecke-Mahler series ∑∞n=0f(⌊nθ+α⌋)β−n, where f(x)∈Z[x] is a non-constant polynomial α is a real number, θ is an irrational real number, and β is an algebraic number such that |β|>1. |
| spellingShingle | Luca, F Ouaknine, J Worrell, JB Transcendence of Hecke-Mahler series |
| title | Transcendence of Hecke-Mahler series |
| title_full | Transcendence of Hecke-Mahler series |
| title_fullStr | Transcendence of Hecke-Mahler series |
| title_full_unstemmed | Transcendence of Hecke-Mahler series |
| title_short | Transcendence of Hecke-Mahler series |
| title_sort | transcendence of hecke mahler series |
| work_keys_str_mv | AT lucaf transcendenceofheckemahlerseries AT ouakninej transcendenceofheckemahlerseries AT worrelljb transcendenceofheckemahlerseries |