{"id":"https://openalex.org/W7225786333","doi":"https://doi.org/10.5281/zenodo.24143383","title":"A uniform lower bound for the degree-scaled L2 height","display_name":"A uniform lower bound for the degree-scaled L2 height","publication_year":2026,"publication_date":"2026-11-12","ids":{"openalex":"https://openalex.org/W7225786333","doi":"https://doi.org/10.5281/zenodo.24143383"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24143383","doi":"https://doi.org/10.5281/zenodo.24143383","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24143383","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24143383","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161421003","display_name":"shou","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"shou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161421003"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.7304999828338623,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.7304999828338623,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.21610000729560852,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.02070000022649765,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8654000163078308},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6883000135421753},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5730999708175659},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5428000092506409},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5270000100135803},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4948999881744385},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46630001068115234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4609000086784363},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3644999861717224},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3427000045776367},{"id":"https://openalex.org/C102607178","wikidata":"https://www.wikidata.org/wiki/Q102761","display_name":"Least common multiple","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2671999931335449}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24143383","doi":"https://doi.org/10.5281/zenodo.24143383","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24143383","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24143384","doi":"https://doi.org/10.5281/zenodo.24143384","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24143384","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24143383","doi":"https://doi.org/10.5281/zenodo.24143383","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24143383","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"a":[1,27,39,47,62],"nonzero":[2],"algebraic":[3,103],"number":[4],"alpha":[5,36],"of":[6,29,41,57,88,105],"degree":[7,68,106],"d,":[8],"let":[9],"h_2(alpha)":[10],"be":[11],"its":[12],"normalized":[13],"all-place":[14],"quadratic":[15,55],"logarithmic":[16],"height":[17,86],"and":[18,54,75,90,136,158],"put":[19],"m_2(alpha)":[20,32],"=":[21],"d":[22,107],"h_2(alpha).":[23],"This":[24,141],"preprint":[25],"gives":[26],"proof":[28],"the":[30,83,163],"bound":[31],">=":[33,99],"sqrt(log(2)/5)":[34],"when":[35],"is":[37,142,154],"not":[38,120],"root":[40],"unity.":[42],"The":[43,80,92,117,134],"reciprocal-unit":[44],"argument":[45],"combines":[46],"modulo-8":[48],"power":[49],"congruence,":[50],"integral":[51],"Pade":[52],"approximants":[53],"divisibility":[56],"rectangular":[58],"Hankel":[59],"minors":[60],"with":[61],"trace-plane":[63],"logarithmic-capacity":[64],"estimate.":[65],"A":[66,101],"twisted":[67],"descent":[69],"removes":[70],"square-radical":[71],"exceptions;":[72],"nonreciprocal":[73],"units":[74],"nonunits":[76],"are":[77],"treated":[78],"separately.":[79],"result":[81],"addresses":[82],"p=2":[84],"degree-scaled":[85],"formulation":[87],"Fili":[89],"Miner.":[91],"same":[93],"constant":[94],"holds":[95],"for":[96],"all":[97],"p":[98],"2.":[100],"reciprocal":[102],"integer":[104],"has":[108],"house":[109],"at":[110],"least":[111],"exp(sqrt(log(2)/5)/d),":[112],"without":[113],"excluding":[114],"unit-circle":[115],"conjugates.":[116],"paper":[118],"does":[119],"prove":[121],"classical":[122],"Lehmer\u2019s":[123],"conjecture.":[124],"Version":[125,132],"2":[126],"incorporates":[127],"comments":[128],"on":[129],"an":[130,143],"internal":[131],"1.":[133],"research":[135],"writing":[137],"were":[138],"substantially":[139],"AI-assisted.":[140],"unrefereed":[144],"preprint:":[145],"no":[146],"complete":[147],"expert":[148],"human":[149],"verification":[150],"or":[151],"proof-assistant":[152],"formalization":[153],"documented.":[155],"LaTeX":[156],"sources":[157],"reproducible":[159],"finite":[160],"checks":[161],"accompany":[162],"PDF.":[164]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
