{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:20:21Z","timestamp":1754144421115,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,6,23]]},"abstract":"<jats:p>The Riemann zeta function, and more generally the L-functions of Dirichlet characters, are among the central objects of study in number theory. We report on a project to formalize the theory of these objects in Lean's &amp;quot;Mathlib&amp;quot; library, including a proof of Dirichlet's theorem on primes in arithmetic progressions and a formal statement of the Riemann hypothesis<\/jats:p><jats:p>Final version, to appear in Annals of Formalized Mathematics<\/jats:p>","DOI":"10.46298\/afm.15328","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T14:50:17Z","timestamp":1752591017000},"source":"Crossref","is-referenced-by-count":0,"title":["Formalizing zeta and L-functions in Lean"],"prefix":"10.46298","volume":"Volume 1","author":[{"given":"David","family":"Loeffler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Stoll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,7,15]]},"container-title":["Annals of Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2503.00959v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2503.00959v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T14:50:17Z","timestamp":1752591017000},"score":1,"resource":{"primary":{"URL":"https:\/\/afm.episciences.org\/15328"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/afm.15328","relation":{"has-preprint":[{"id-type":"arxiv","id":"2503.00959v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2503.00959v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2503.00959","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2503.00959","asserted-by":"subject"}]},"subject":[],"published":{"date-parts":[[2025,7,15]]},"article-number":"15328"}}