{"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/an-elementary-bound-on-siegel-zeroes","title":"An elementary bound on Siegel zeroes","arxiv_id":"1811.12521","date":"2018-11-29","proceeding":null,"authors":["Thomas Morrill","Tim Trudgian"],"abstract":"We consider Dirichlet $L$-functions $L(s, \\chi)$ where $\\chi$ is a real, non-principal character modulo $q$. Using Pintz's refinement of Page's theorem, we prove that for $q\\geq 3$ the function $L(s, \\chi)$ has at most one real zero $\\beta$ with $1- 1.011/\\log q < \\beta < 1$.","url_abs":"http://arxiv.org/abs/1811.12521v1","url_pdf":"http://arxiv.org/pdf/1811.12521v1.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":"an-elementary-bound-on-siegel-zeroes","repo_url":"https://github.com/tsmorrill/Pintz","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}