{"journal":{"journal_metadata":{"@language":"en","full_title":"Discrete Mathematics & Theoretical Computer Science","issn":{"@media_type":"electronic","value":"1365-8050"}},"journal_issue":{"publication_date":{"@media_type":"online","month":"01","day":"01","year":"2003"},"journal_volume":{"volume":"Vol. 6 no. 1"}},"journal_article":{"@publication_type":"full_text","@language":"en","titles":{"title":"An application of results by Hardy, Ramanujan and Karamata to Ackermannian functions"},"contributors":{"person_name":{"@sequence":"first","@contributor_role":"author","given_name":"Andreas","surname":"Weiermann","affiliations":{"institution":{"institution_name":"Mathematical Institute"}},"ORCID":"https://orcid.org/0000-0002-5561-5323"}},"abstract":{"value":{"@xml:lang":"en","value":"The Ackermann function is a fascinating and well studied paradigm for a function which eventually dominates all primitive recursive functions. By a classical result from the theory of recursive functions it is known that the Ackermann function can be defined by an unnested or descent recursion along the segment of ordinals below ω ^ω (or equivalently along the order type of the polynomials under eventual domination). In this article we give a fine structure analysis of such a Ackermann type descent recursion in the case that the ordinals below ω ^ω are represented via a Hardy Ramanujan style coding. This paper combines number-theoretic results by Hardy and Ramanujan, Karamata's celebrated Tauberian theorem and techniques from the theory of computability in a perhaps surprising way."}},"publication_date":{"@media_type":"online","month":"01","day":"01","year":"2003"},"acceptance_date":{"@media_type":"online","month":"06","day":"09","year":"2015"},"publisher_item":{"item_number":{"@item_number_type":"article_number","value":"339"}},"program":[{"@name":"AccessIndicators","free_to_read":{"@start_date":"2003-01-01","value":""},"license_ref":[{"@applies_to":"am","@start_date":"2003-01-01","value":"https://about.hal.science/hal-authorisation-v1"},{"@applies_to":"vor","@start_date":"2003-01-01","value":"https://about.hal.science/hal-authorisation-v1"},{"@applies_to":"tdm","@start_date":"2003-01-01","value":"https://about.hal.science/hal-authorisation-v1"}]},{"related_item":{"intra_work_relation":{"@identifier-type":"uri","@relationship-type":"isSameAs","value":"https://hal.science/hal-00958996v1"}}}],"doi_data":{"doi":"10.46298/dmtcs.339","resource":"https://dmtcs.episciences.org/339","collection":[{"@property":"crawler-based","item":{"@crawler":"iParadigms","resource":"https://hal.science/hal-00958996v1/document"}},{"@property":"text-mining","item":{"resource":{"@mime_type":"application/pdf","value":"https://hal.science/hal-00958996v1/document"}}}]},"keywords":{"en":["Ackermann function","Karamata's theorem","Hardy Ramanujan methods","analytic combinatorics"],"0":"[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]"}}},"database":{"current":{"mainPdfUrl":"https://hal.science/hal-00958996v1/document","original_language":"en","identifiers":{"permanent_item_number":339,"document_item_number":339,"repository_identifier":"hal-00958996","concept_identifier":null},"isTmp":false,"flag":"imported","type":{"title":"article"},"status":{"id":16,"label":{"en":"published","fr":"publié"}},"url":"https://dmtcs.episciences.org/339","version":1,"files":{"link":"https://dmtcs.episciences.org/339/pdf"},"dates":{"first_submission_date":"2015-03-26 16:18:36","posted_date":"2015-03-26 16:18:36","modification_date":"2025-03-31 21:04:04","publication_date":"2003-01-01 08:00:00"},"volume":{"id":77,"position":"66","number":null,"year":null,"has_proceedings":false,"titles":{"en":"Vol. 6 no. 1"},"descriptions":null,"bibliographical_references":null,"settings":{"is_current_issue":false,"is_special_issue":false,"is_open":false}},"position_in_volume":8,"section":null,"journal":{"id":1,"code":"dmtcs","name":"Discrete Mathematics & Theoretical Computer Science","url":"https://dmtcs.episciences.org"},"repository":{"id":"1","name":"HAL","type":"repository","status":"1","identifier":"oai:HAL:hal-00958996v1","base_url":"https://api.archives-ouvertes.fr/oai/hal/","doi_prefix":"","api_url":"https://api.archives-ouvertes.fr","doc_url":"https://hal.science/hal-00958996v1","paper_url":"https://hal.science/hal-00958996v1/document"},"cited_by":{"1058":{"id":"1058","citation":"{\"0\":{\"type\":null,\"author\":\"Andreas Weiermann, 0000-0002-5561-5323\",\"year\":2008,\"title\":\"Phase transitions for Gödel incompleteness\",\"event_place\":\"\",\"source_title\":\"Ghent University Academic Bibliography (Ghent University)\",\"volume\":\"157\",\"issue\":\"2-3\",\"page\":\"281-296\",\"doi\":\"10.1016/j.apal.2008.09.012\",\"oa_link\":\"http://hdl.handle.net/1854/LU-547549\"}}","docid":"339","source_id":"13","updated_at":"2026-01-24 05:36:19","source_id_name":"OpenCitations"}},"classifications":[],"graphical_abstract_file":"","metrics":{"page_count":"657","file_count":"886"}},"latest_version_item_number":339,"first_version_item_number":339,"previous_versions":null}}