{"id":"https://openalex.org/W7213353958","doi":"https://doi.org/10.48550/arxiv.2609.15329","title":"Optimising Selberg's method for critical zeros","display_name":"Optimising Selberg's method for critical zeros","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213353958","doi":"https://doi.org/10.48550/arxiv.2609.15329"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15329","pdf_url":"https://arxiv.org/pdf/2609.15329","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15329","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048472565","display_name":"Andrew Pearce\u2010Crump","orcid":"https://orcid.org/0000-0002-1879-5599","observed_orcids":["https://orcid.org/0000-0002-1879-5599"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pearce-Crump, Andrew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048472565"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.9300000071525574},{"id":"https://openalex.org/keywords/critical-zeros","display_name":"critical zeros","score":0.8330000042915344},{"id":"https://openalex.org/keywords/zeros-on-the-critical-line","display_name":"zeros on the critical line","score":0.8159999847412109},{"id":"https://openalex.org/keywords/nontrivial-zeros","display_name":"non-trivial zeros","score":0.7329999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7853999733924866},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.5522000193595886},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C2776605787","wikidata":"https://www.wikidata.org/wiki/Q5186739","display_name":"Critical line","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4077000021934509},{"id":"https://openalex.org/C111993293","wikidata":"https://www.wikidata.org/wiki/Q8063364","display_name":"Z function","level":4,"score":0.3734999895095825},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3264999985694885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30790001153945923},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.295199990272522},{"id":"https://openalex.org/C30573924","wikidata":"https://www.wikidata.org/wiki/Q905326","display_name":"Digamma function","level":5,"score":0.28630000352859497},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C203513110","wikidata":"https://www.wikidata.org/wiki/Q1073118","display_name":"Particular values of Riemann zeta function","level":5,"score":0.2639999985694885}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15329","pdf_url":"https://arxiv.org/pdf/2609.15329","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.15329","doi":"https://doi.org/10.48550/arxiv.2609.15329","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15329","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15329","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15329","pdf_url":"https://arxiv.org/pdf/2609.15329","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213353958.pdf","grobid_xml":"https://content.openalex.org/works/W7213353958.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2093171821","https://openalex.org/W2946615458","https://openalex.org/W3094198207","https://openalex.org/W7075994136","https://openalex.org/W7203614468","https://openalex.org/W7207551484"],"related_works":["https://openalex.org/W2053752128","https://openalex.org/W32649130","https://openalex.org/W4288091054","https://openalex.org/W2963814182","https://openalex.org/W2804675377","https://openalex.org/W2291317981","https://openalex.org/W64285022","https://openalex.org/W7203605068","https://openalex.org/W71812887","https://openalex.org/W7147448100"],"abstract_inverted_index":{"We":[0],"revisit":[1],"Zhuravlev's":[2,22],"1974":[3],"quantitative":[4],"form":[5],"of":[6,13,38,53,71,75],"Selberg's":[7,64],"sign-change":[8],"method":[9,55],"for":[10],"the":[11,14,19,31,46,51,54,58,72,76,82],"zeros":[12,74],"Riemann":[15,77],"zeta":[16,78],"function":[17,79],"on":[18,81],"critical":[20,83],"line.":[21,84],"work,":[23],"originally":[24],"in":[25,30],"Russian":[26],"and":[27,56],"little":[28],"known":[29,62],"West,":[32],"established":[33],"an":[34],"explicit":[35],"positive":[36],"proportion":[37],"such":[39],"zeros.":[40],"Using":[41],"modern":[42],"techniques":[43],"we":[44],"optimise":[45],"arithmetic":[47],"mean":[48],"value":[49],"at":[50],"heart":[52],"obtain":[57],"strongest":[59],"result":[60],"yet":[61],"from":[63],"method,":[65],"proving":[66],"that":[67],"more":[68],"than":[69],"$6.78\\%$":[70],"non-trivial":[73],"lie":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}