{"id":13992987,"url":"https://github.com/bhgomes/lean-riemann-hypothesis","last_synced_at":"2025-08-31T05:33:33.053Z","repository":{"id":105903864,"uuid":"275204877","full_name":"bhgomes/lean-riemann-hypothesis","owner":"bhgomes","description":"Riemann Hypothesis in Lean","archived":false,"fork":false,"pushed_at":"2021-03-03T07:18:32.000Z","size":1852,"stargazers_count":40,"open_issues_count":0,"forks_count":7,"subscribers_count":3,"default_branch":"master","last_synced_at":"2025-03-22T05:16:54.153Z","etag":null,"topics":["lean","lean-theorem-prover","mathlib","riemann-hypothesis"],"latest_commit_sha":null,"homepage":"https://reu.dimacs.rutgers.edu/~bg441/","language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/bhgomes.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null}},"created_at":"2020-06-26T16:52:34.000Z","updated_at":"2025-02-20T11:00:25.000Z","dependencies_parsed_at":"2024-01-18T04:09:56.666Z","dependency_job_id":"6dc7dce5-c239-4ea4-94cf-56c8bc77c563","html_url":"https://github.com/bhgomes/lean-riemann-hypothesis","commit_stats":null,"previous_names":[],"tags_count":1,"template":false,"template_full_name":null,"purl":"pkg:github/bhgomes/lean-riemann-hypothesis","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bhgomes%2Flean-riemann-hypothesis","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bhgomes%2Flean-riemann-hypothesis/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bhgomes%2Flean-riemann-hypothesis/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bhgomes%2Flean-riemann-hypothesis/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/bhgomes","download_url":"https://codeload.github.com/bhgomes/lean-riemann-hypothesis/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bhgomes%2Flean-riemann-hypothesis/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":272940861,"owners_count":25018983,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-08-31T02:00:09.071Z","response_time":79,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["lean","lean-theorem-prover","mathlib","riemann-hypothesis"],"created_at":"2024-08-09T14:02:11.767Z","updated_at":"2025-08-31T05:33:32.974Z","avatar_url":"https://github.com/bhgomes.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"# Riemann Hypothesis in Lean\n\n[![DOI](https://zenodo.org/badge/275204877.svg)](https://zenodo.org/badge/latestdoi/275204877)\n\n_by Brandon H. Gomes and Alex Kontorovich through the Department of Mathematics, Rutgers University_\n\n## Formalization\n\nThe Riemann Hypothesis is formalized by assuming some algebraic properties of the real and complex numbers and the existence/properties of the complex exponential function and the real logarithm. These axioms are then used to construct the Dirichlet η function which we use to define the Riemann Hypothesis as the following type:\n\n```lean\n(Re s ∈ (0,1)) ∧ (eta s = 0) → (Re s = 1/2)\n```\n\nWe also include the file, [`mathlib/impl.lean`](src/mathlib/impl.lean), which is a witness that the axioms can be proved using [`mathlib`](https://github.com/leanprover-community/mathlib).\n\n## Acknowledgements\n\nWe would like to thank Alex Best, Kevin Buzzard, Colin Fan, Sebastien Gouezel, Heather Macbeth, and the Zulip Lean community for many suggestions that made this project possible.\n\nThe work of the first-named author was supported by the Rutgers Math Department through the DIMACS REU, and both are supported in part by the second-named author's NSF grant DMS-1802119.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbhgomes%2Flean-riemann-hypothesis","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fbhgomes%2Flean-riemann-hypothesis","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbhgomes%2Flean-riemann-hypothesis/lists"}