{"id":"https://openalex.org/W7212584868","doi":"https://doi.org/10.48550/arxiv.2609.12427","title":"Polynomial growth of Bohnenblust--Hille constants on the Hamming cube","display_name":"Polynomial growth of Bohnenblust--Hille constants on the Hamming cube","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212584868","doi":"https://doi.org/10.48550/arxiv.2609.12427"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12427","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12427","pdf_url":"https://arxiv.org/pdf/2609.12427","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/2609.12427","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033685269","display_name":"Paata Ivanisvili","orcid":"https://orcid.org/0000-0002-0644-9090","observed_orcids":["https://orcid.org/0000-0002-0644-9090"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ivanisvili, Paata","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5033685269"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.33809998631477356,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.33809998631477356,"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"}},{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.1298999935388565,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.12160000205039978,"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/hamming-cube","display_name":"Hamming cube","score":0.9929999709129333},{"id":"https://openalex.org/keywords/polynomial-growth","display_name":"polynomial growth","score":0.7599999904632568},{"id":"https://openalex.org/keywords/uniform-bounds","display_name":"uniform bounds","score":0.3540000021457672},{"id":"https://openalex.org/keywords/fourier-coefficients","display_name":"Fourier coefficients","score":0.5450000166893005},{"id":"https://openalex.org/keywords/multilinear-forms","display_name":"multilinear forms","score":0.5450000166893005},{"id":"https://openalex.org/keywords/hypercontractivity","display_name":"hypercontractivity","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7264999747276306},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6807000041007996},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6678000092506409},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6367999911308289},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6083999872207642},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.5920000076293945},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.5162000060081482},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44909998774528503},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.36149999499320984},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2847000062465668}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12427","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12427","pdf_url":"https://arxiv.org/pdf/2609.12427","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.2609.12427","doi":"https://doi.org/10.48550/arxiv.2609.12427","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12427","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:2609.12427","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12427","pdf_url":"https://arxiv.org/pdf/2609.12427","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":[{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7796262111","display_name":"CAREER: Discrete Structures and Orthogonal Systems","funder_award_id":"2152401","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212584868.pdf","grobid_xml":"https://content.openalex.org/works/W7212584868.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1524383063","https://openalex.org/W1969714776","https://openalex.org/W2094654291","https://openalex.org/W2130170517","https://openalex.org/W2334237942","https://openalex.org/W2625960977","https://openalex.org/W2964256713","https://openalex.org/W3201120038","https://openalex.org/W4233413206","https://openalex.org/W4385198809","https://openalex.org/W7203694766"],"related_works":["https://openalex.org/W7203694766","https://openalex.org/W316486477","https://openalex.org/W1570957364","https://openalex.org/W1738461656","https://openalex.org/W7212087388","https://openalex.org/W2949710862","https://openalex.org/W2111529031","https://openalex.org/W7213881609","https://openalex.org/W2963410552","https://openalex.org/W2963558775"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,29],"the":[3,10,18,53],"Bohnenblust--Hille":[4],"constants":[5],"for":[6],"Walsh":[7],"polynomials":[8],"on":[9],"Hamming":[11],"cube":[12],"grow":[13],"at":[14,37],"most":[15,38],"polynomially":[16],"in":[17,52],"degree.":[19],"More":[20],"precisely,":[21],"there":[22],"is":[23,50,58],"an":[24],"absolute":[25],"constant":[26],"$K$":[27],"such":[28],"every":[30],"$f":[31],":\\{-1,1\\}^{n}":[32],"\\to":[33],"\\mathbb{C}$":[34],"of":[35],"degree":[36],"$m$":[39],"satisfies":[40],"$$":[41,47],"\\left(\\sum_{|S|\\le":[42],"m}|\\widehat":[43],"f(S)|^{2m/(m+1)}\\right)^{(m+1)/(2m)}":[44],"\\le":[45],"Km^{27}\\|f\\|_\\infty.":[46],"The":[48,55],"estimate":[49],"uniform":[51],"dimension.":[54],"exponent":[56],"$27$":[57],"not":[59],"optimized.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}