{"id":"https://openalex.org/W7204851823","doi":"https://doi.org/10.48550/arxiv.2608.27732","title":"Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions","display_name":"Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204851823","doi":"https://doi.org/10.48550/arxiv.2608.27732"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27732","pdf_url":"https://arxiv.org/pdf/2608.27732","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":"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/2608.27732","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101801544","display_name":"Thomas Wright","orcid":"https://orcid.org/0000-0001-7130-187X","observed_orcids":["https://orcid.org/0000-0001-7130-187X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wright, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101801544"],"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0,"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/equidistribution","display_name":"equidistribution","score":0.46299999952316284},{"id":"https://openalex.org/keywords/multiplicative-convolution","display_name":"multiplicative convolution","score":0.4059999883174896},{"id":"https://openalex.org/keywords/subconvex-bounds","display_name":"subconvex bounds","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C34282223","wikidata":"https://www.wikidata.org/wiki/Q6421354","display_name":"Kloosterman sum","level":2,"score":0.9161999821662903},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.8960000276565552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8938999772071838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5285000205039978},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32679998874664307},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2660999894142151},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.26030001044273376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27732","pdf_url":"https://arxiv.org/pdf/2608.27732","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.27732","doi":"https://doi.org/10.48550/arxiv.2608.27732","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27732","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:2608.27732","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27732","pdf_url":"https://arxiv.org/pdf/2608.27732","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":"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/W7204851823.pdf","grobid_xml":"https://content.openalex.org/works/W7204851823.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7158066412","https://openalex.org/W1633102314","https://openalex.org/W3170844762","https://openalex.org/W2070099638","https://openalex.org/W2900670684","https://openalex.org/W2995830213","https://openalex.org/W3213061765","https://openalex.org/W4376135306","https://openalex.org/W2514166785","https://openalex.org/W2763934463"],"abstract_inverted_index":{"This":[0],"paper":[1],"broadens":[2],"the":[3,93,98],"range":[4],"on":[5,11,25,86],"which":[6,69],"Fouvry":[7,71],"and":[8,20,28,38,63,72,82],"Radziwi\u0142\u0142's":[9,73],"results":[10],"nearly":[12],"balanced":[13],"convolutions":[14],"apply.":[15],"In":[16],"particular,":[17],"let":[18,39],"$\u03b1_m$":[19],"$\u03b2_n$":[21,32],"be":[22],"sequences":[23],"supported":[24],"$m\\sim":[26],"M$":[27],"$n\\sim":[29],"N$":[30],"where":[31,95],"is":[33],"equidistributed":[34],"for":[35],"small":[36],"moduli,":[37],"$Q=X^{\\frac":[40],"12+\\varepsilon}$.":[41],"We":[42],"find":[43],"that":[44],"\\begin{gather*}\\sum_{q\\sim":[45],"Q}\\left|\\mathop{\\sum\\sum}_{\\substack{n\\sim":[46],"N,m\\sim":[47,53],"M":[48,54],"\\\\":[49,55],"mn\\equiv":[50],"a\\pmod":[51],"q}}\u03b1_m\u03b2_n-\\frac{1}{\u03d5(q)}\\mathop{\\sum\\sum}_{\\substack{n\\sim":[52],"(mn,q)=1}}\u03b1_m\u03b2_n\\right|\\ll":[56],"\\frac{X}{\\log^A":[57],"X}":[58],"\\end{gather*}":[59],"if":[60],"$N=X^{\\frac":[61],"12+\u03b4}$":[62],"$M=X^{\\frac":[64],"12-\u03b4}$":[65],"with":[66,89],"$0<\u03b4<\\frac":[67,74],"1{68}$,":[68],"improves":[70],"1{112}$.":[75],"To":[76],"prove":[77],"this,":[78],"we":[79],"sharpen":[80],"Bettin":[81],"Chandee's":[83],"famous":[84],"result":[85],"trilinear":[87],"forms":[88],"Kloosterman":[90],"fractions":[91],"in":[92],"case":[94],"some":[96],"of":[97],"sums":[99],"are":[100],"over":[101],"subdyadic":[102],"intervals.":[103]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-01T00:00:00"}