{"id":"https://openalex.org/W7127580912","doi":"https://doi.org/10.48550/arxiv.2602.03289","title":"On the Summability Problem of Multivariate Rational Functions in the Mixed Case","display_name":"On the Summability Problem of Multivariate Rational Functions in the Mixed Case","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127580912","doi":"https://doi.org/10.48550/arxiv.2602.03289"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.03289","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070141631","display_name":"Shaoshi Chen","orcid":"https://orcid.org/0000-0001-8756-3006"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Shaoshi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101124191","display_name":"Lixin Du","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Lixin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080338552","display_name":"Hanqian Fang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fang, Hanqian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122023450","display_name":"Yisen Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yisen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070141631"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.3084000051021576,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.3084000051021576,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.19689999520778656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.09870000183582306,"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/multivariate-statistics","display_name":"Multivariate statistics","score":0.7700999975204468},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5963000059127808},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5059999823570251},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.44940000772476196},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"Multivariate analysis","score":0.41359999775886536},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3490000069141388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7767000198364258},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7700999975204468},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5963000059127808},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5059999823570251},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.44940000772476196},{"id":"https://openalex.org/C38180746","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate analysis","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.376800000667572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36880001425743103},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2651999890804291},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C3019018024","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear operators","level":3,"score":0.2565000057220459},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.03289","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.03289","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.03289","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.03289","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Continuing":[0],"previous":[1],"work,":[2],"this":[3],"paper":[4],"focuses":[5],"on":[6,31],"the":[7,15,46,50],"summability":[8,28],"problem":[9],"of":[10,49,60],"multivariate":[11,61],"rational":[12,47],"functions":[13],"in":[14,18],"mixed":[16],"case":[17,48],"which":[19],"both":[20],"shift":[21],"and":[22,40],"$q$-shift":[23],"operators":[24],"can":[25],"appear.":[26],"Our":[27],"criteria":[29],"rely":[30],"three":[32],"ingredients":[33],"including":[34],"orbital":[35],"decompositions,":[36],"Sato's":[37],"isotropy":[38],"groups,":[39],"difference":[41],"transformations.":[42],"This":[43],"work":[44],"settles":[45],"long-term":[51],"project":[52],"aimed":[53],"at":[54],"developing":[55],"algorithms":[56],"for":[57],"symbolic":[58],"summation":[59],"functions.":[62]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-06T00:00:00"}
