{"id":"https://openalex.org/W7212285298","doi":"https://doi.org/10.48550/arxiv.2609.11888","title":"The asymptotic in Waring's problem over function fields beyond twice the degree","display_name":"The asymptotic in Waring's problem over function fields beyond twice the degree","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212285298","doi":"https://doi.org/10.48550/arxiv.2609.11888"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11888","pdf_url":"https://arxiv.org/pdf/2609.11888","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/2609.11888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017948886","display_name":"Matthew Hase-Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hase-Liu, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017948886"],"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":0.975600004196167,"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":0.975600004196167,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.01860000006854534,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.00419999985024333,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/waring-s-problem","display_name":"Waring's problem","score":0.9919999837875366},{"id":"https://openalex.org/keywords/function-fields","display_name":"function fields","score":0.9010000228881836},{"id":"https://openalex.org/keywords/polynomials-over-finite-fields","display_name":"polynomials over finite fields","score":0.8529999852180481},{"id":"https://openalex.org/keywords/asymptotic-counting","display_name":"asymptotic counting","score":0.7229999899864197},{"id":"https://openalex.org/keywords/intersection-theory","display_name":"intersection theory","score":0.824999988079071},{"id":"https://openalex.org/keywords/singular-set","display_name":"singular set","score":0.9459999799728394},{"id":"https://openalex.org/keywords/parameter-space","display_name":"parameter space","score":0.6129999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8269000053405762},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.6424999833106995},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6222000122070312},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5902000069618225},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5511000156402588},{"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/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4869000017642975},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4519999921321869},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41760000586509705},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3953999876976013},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.29409998655319214},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11888","pdf_url":"https://arxiv.org/pdf/2609.11888","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.2609.11888","doi":"https://doi.org/10.48550/arxiv.2609.11888","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11888","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11888","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11888","pdf_url":"https://arxiv.org/pdf/2609.11888","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/W7212285298.pdf","grobid_xml":"https://content.openalex.org/works/W7212285298.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4391940789","https://openalex.org/W7204595847"],"related_works":["https://openalex.org/W2963159955","https://openalex.org/W4405876269","https://openalex.org/W2017088705","https://openalex.org/W2955063882","https://openalex.org/W4321492523","https://openalex.org/W2010191335","https://openalex.org/W2313657395","https://openalex.org/W2085169541","https://openalex.org/W138965881","https://openalex.org/W1981289252"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,17,37,42,60,73,76,85],"expected":[3,38],"asymptotic":[4,39],"in":[5,34,41,93],"Waring's":[6],"problem":[7],"over":[8],"$\\mathbb":[9],"F_q[T]$,":[10],"with":[11],"a":[12],"power-saving":[13],"error,":[14],"whenever":[15],"$n>2d$,":[16],"characteristic":[18],"is":[19,32,49,91],"greater":[20],"than":[21],"$(d-1)^2$,":[22],"and":[23,67],"$q$":[24,90],"satisfies":[25],"an":[26,50],"explicit":[27],"lower":[28,87],"bound.":[29],"This":[30],"range":[31],"sharp":[33],"general":[35],"for":[36],"uniformly":[40],"target":[43],"polynomial.":[44],"Our":[45],"main":[46],"new":[47],"input":[48],"aggregate":[51],"minor":[52],"arc":[53],"estimate:":[54],"we":[55],"count":[56],"functionals":[57],"according":[58],"to":[59,71],"codimension":[61],"of":[62,75,95],"their":[63],"associated":[64],"singular":[65],"loci":[66],"use":[68],"intersection":[69],"theory":[70],"bound":[72,88],"degrees":[74],"resulting":[77],"parameter":[78],"spaces.":[79],"In":[80],"particular,":[81],"if":[82],"$n\\ge":[83],"(2+\\varepsilon)d$,":[84],"required":[86],"on":[89],"polynomial":[92],"$d$":[94],"degree":[96],"$2+4/\\varepsilon$.":[97]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}