{"id":"https://openalex.org/W7220948623","doi":"https://doi.org/10.48550/arxiv.2610.08424","title":"On S\u00e1rk\u00f6zy's Local Extrema Conjectures","display_name":"On S\u00e1rk\u00f6zy's Local Extrema Conjectures","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220948623","doi":"https://doi.org/10.48550/arxiv.2610.08424"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08424","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08424","pdf_url":"https://arxiv.org/pdf/2610.08424","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08424","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007200290","display_name":"Alexander P. Mangerel","orcid":"https://orcid.org/0000-0003-4055-4078","observed_orcids":["https://orcid.org/0000-0003-4055-4078"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mangerel, Alexander P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5007200290"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/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":9.999999747378752e-05,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/multiplicative-functions","display_name":"multiplicative functions","score":0.9580000042915344},{"id":"https://openalex.org/keywords/additive-functions","display_name":"additive functions","score":0.8130000233650208},{"id":"https://openalex.org/keywords/local-maxima","display_name":"local maxima","score":0.8840000033378601},{"id":"https://openalex.org/keywords/local-minima","display_name":"local minima","score":0.9990000128746033},{"id":"https://openalex.org/keywords/logarithmic-density","display_name":"logarithmic density","score":0.9089999794960022},{"id":"https://openalex.org/keywords/pretentiousness","display_name":"pretentiousness","score":0.7080000042915344}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8535000085830688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.832099974155426},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.597000002861023},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.548799991607666},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49160000681877136},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.414000004529953},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.392300009727478},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37369999289512634},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08424","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08424","pdf_url":"https://arxiv.org/pdf/2610.08424","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.2610.08424","doi":"https://doi.org/10.48550/arxiv.2610.08424","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08424","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:2610.08424","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08424","pdf_url":"https://arxiv.org/pdf/2610.08424","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220948623.pdf","grobid_xml":"https://content.openalex.org/works/W7220948623.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1495341057","https://openalex.org/W2731160740","https://openalex.org/W4388927454","https://openalex.org/W4394640939","https://openalex.org/W7015509177","https://openalex.org/W7171390441","https://openalex.org/W3198113772","https://openalex.org/W1990973287","https://openalex.org/W7160296622","https://openalex.org/W4415227423"],"abstract_inverted_index":{"Let":[0],"$f:":[1,88],"\\mathbb{N}":[2,89],"\\rightarrow":[3,90],"(0,\\infty)$":[4],"be":[5,168],"a":[6,62,72,107,123,151],"multiplicative":[7,69,86],"function,":[8],"and":[9,37],"let":[10],"$\u03c9>":[11],"0$.":[12],"We":[13],"consider":[14],"the":[15,21,34,45,133,139,146,155,158],"frequency":[16],"with":[17],"which":[18,166],"patterns":[19,55],"of":[20,47,49,53,65,112,138,157,161,169],"form":[22],"$$":[23,31],"f(n)":[24,28],">":[25],"\u03c9\\max\\{f(n-1),f(n+1)\\},":[26],"\\quad":[27],"<":[29],"\\frac{1}\u03c9\\min\\{f(n-1),f(n+1)\\}":[30],"occur":[32],"in":[33,106,132],"sequence":[35],"$(f(n))_n$,":[36],"give":[38],"necessary":[39],"conditions":[40],"on":[41,122],"$f$":[42],"so":[43],"that":[44,92],"set":[46],"occurrences":[48],"at":[50],"least":[51],"one":[52],"these":[54],"has":[56],"logarithmic":[57],"density":[58],"$0$.":[59],"This":[60,104],"includes":[61],"complete":[63],"classification":[64],"all":[66,85],"such":[67],"completely":[68],"functions.":[70,129],"As":[71],"particular":[73],"application,":[74],"we":[75],"characterise":[76],"(up":[77],"to":[78,145],"prime":[79],"powers":[80],"$p^k$,":[81],"$k":[82],"\\geq":[83],"2$)":[84],"functions":[87],"\\mathbb{N}$":[91],"have":[93],"either":[94],"finitely":[95,100],"many":[96,101],"local":[97,102],"maxima,":[98],"or":[99],"minima.":[103],"answers,":[105],"strong":[108],"form,":[109],"two":[110],"conjectures":[111],"A.":[113],"S\u00e1rk\u00f6zy":[114],"from":[115],"2001.":[116],"\\\\":[117],"The":[118],"proof":[119],"is":[120],"based":[121],"natural":[124],"``pretentiousness''":[125],"dichotomy":[126],"for":[127,141,154],"additive":[128,142,163],"Key":[130],"tools":[131],"analysis":[134],"include":[135],"an":[136,162],"analogue":[137],"Matom\u00e4ki-Radziwi\u0142\u0142theorem":[140],"functions,":[143],"due":[144],"author,":[147],"as":[148,150],"well":[149],"new":[152],"bound":[153],"concentration":[156],"gaps":[159],"$g(n+1)-g(n)$":[160],"function":[164],"$g$,":[165],"may":[167],"independent":[170],"interest.":[171]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-09T00:00:00"}