{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-constant-terms-of-certain-meromorphic","title":"On the constant terms of certain meromorphic modular forms for Hecke groups","arxiv_id":"2212.12515","date":"2022-12-23","proceeding":null,"authors":["Barry Brent"],"abstract":"We study polynomials interpolating the (rational) constant terms of certain meromorphic modular forms for Hecke groups. We make observations about the divisibility properties of the constant terms and connect them to several sequences, for example, to O.E.I.S. sequence A005148 \\cite{OEISNewmanShanks}, which was studied by Newman, Shanks and Zagier \\cite{newman2004sequence}, \\cite{newman2004sequenceAppendix} in an article on its use in series approximations to $\\pi$.","url_abs":"https://arxiv.org/abs/2212.12515v1","url_pdf":"https://arxiv.org/pdf/2212.12515v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-constant-terms-of-certain-meromorphic","repo_url":"https://github.com/barry314159a/newmanshanks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}