{"id":"https://openalex.org/W7220649783","doi":"https://doi.org/10.48550/arxiv.2610.05515","title":"The main conjecture for a Vinogradov subsystem","display_name":"The main conjecture for a Vinogradov subsystem","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220649783","doi":"https://doi.org/10.48550/arxiv.2610.05515"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05515","pdf_url":"https://arxiv.org/pdf/2610.05515","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/2610.05515","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074922873","display_name":"Trevor D. Wooley","orcid":"https://orcid.org/0000-0002-8781-4706","observed_orcids":["https://orcid.org/0000-0002-8781-4706"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wooley, Trevor D.","raw_affiliation_strings":["Department of Mathematics , Purdue University , 150 N. University Street , West Lafayette , IN 47907-2067 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Purdue University , 150 N. University Street , West Lafayette , IN 47907-2067 , USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074922873"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9990000128746033,"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":0.9990000128746033,"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":0.00039999998989515007,"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/T12404","display_name":"Mathematical Approximation and Integration","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/exponential-sums","display_name":"exponential sums","score":0.7540000081062317},{"id":"https://openalex.org/keywords/waring-s-problem","display_name":"Waring's problem","score":0.6470000147819519},{"id":"https://openalex.org/keywords/number-fields","display_name":"number fields","score":0.7440000176429749},{"id":"https://openalex.org/keywords/function-fields","display_name":"function fields","score":0.7929999828338623},{"id":"https://openalex.org/keywords/mean-estimation","display_name":"mean estimation","score":0.3880000114440918}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.816100001335144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6880999803543091},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5078999996185303},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42890000343322754},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41200000047683716},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29089999198913574},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05515","pdf_url":"https://arxiv.org/pdf/2610.05515","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.2610.05515","doi":"https://doi.org/10.48550/arxiv.2610.05515","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05515","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:2610.05515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05515","pdf_url":"https://arxiv.org/pdf/2610.05515","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/W7220649783.pdf","grobid_xml":"https://content.openalex.org/works/W7220649783.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2744618969","https://openalex.org/W7096546663","https://openalex.org/W2501621024","https://openalex.org/W1981452459","https://openalex.org/W7220663827","https://openalex.org/W2949746781","https://openalex.org/W7098569679","https://openalex.org/W2951739344","https://openalex.org/W2148559955","https://openalex.org/W2133848721"],"abstract_inverted_index":{"When":[0],"$k\\ge":[1],"2$":[2],"and":[3,72],"$s>0$,":[4],"we":[5],"establish":[6],"that":[7],"for":[8,28],"each":[9],"$\\varepsilon>0$,":[10],"one":[11],"has":[12],"\\[":[13],"\\int_{[0,1)^{k-1}}\\biggl|":[14],"\\sum_{1\\le":[15],"x\\le":[16],"X}e(\u03b1_2x^2+\\ldots":[17],"+\u03b1_k":[18],"x^k)\\biggr|^{2s}\\,{\\rm":[19],"d}\\boldsymbol":[20],"\u03b1\\ll":[21],"X^{s+\\varepsilon}+X^{2s-(k^2+k-2)/2},":[22],"\\]":[23],"confirming":[24],"the":[25,51,54,67],"main":[26],"conjecture":[27],"a":[29],"new":[30],"family":[31],"of":[32,37,50,61,69],"exponential":[33],"sums":[34],"beyond":[35],"those":[36],"Vinogradov":[38],"(translation-dilation":[39],"invariant)":[40],"type.":[41],"Our":[42],"methods":[43],"are":[44],"based":[45],"on":[46],"very":[47],"recent":[48],"work":[49],"author":[52],"employing":[53],"nested":[55],"efficient":[56],"congruencing":[57],"method.":[58],"Consequently,":[59],"analogues":[60],"our":[62],"results":[63],"hold":[64],"also":[65],"in":[66],"setting":[68],"number":[70],"fields":[71],"function":[73],"fields.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}