{"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/distribution-of-integral-fourier-coefficients","title":"Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes","arxiv_id":"0704.0012","date":"2007-03-31","proceeding":null,"authors":["Dohoon Choi"],"abstract":"Recently, Bruinier and Ono classified cusp forms $f(z) := \\sum_{n=0}^{\\infty} a_f(n)q ^n \\in S_{\\lambda+1/2}(\\Gamma_0(N),\\chi)\\cap \\mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \\geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.","url_abs":"http://arxiv.org/abs/0704.0012v1","url_pdf":"http://arxiv.org/pdf/0704.0012v1.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":"distribution-of-integral-fourier-coefficients","repo_url":"https://github.com/miku/xmlcutty","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}