{"id":"https://openalex.org/W7220964100","doi":"https://doi.org/10.48550/arxiv.2610.07227","title":"Systems of equations with elements of finitely generated groups and with linear recurrence sequences","display_name":"Systems of equations with elements of finitely generated groups and with linear recurrence sequences","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220964100","doi":"https://doi.org/10.48550/arxiv.2610.07227"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07227","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07227","pdf_url":"https://arxiv.org/pdf/2610.07227","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/2610.07227","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003873251","display_name":"Subham Bhakta","orcid":"https://orcid.org/0000-0001-9901-8726","observed_orcids":["https://orcid.org/0000-0001-9901-8726"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhakta, Subham","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008253632","display_name":"Alina Ostafe","orcid":"https://orcid.org/0000-0001-7398-0589","observed_orcids":["https://orcid.org/0000-0001-7398-0589"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ostafe, Alina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030033231","display_name":"Igor E. Shparlinski","orcid":"https://orcid.org/0000-0002-5246-9391","observed_orcids":["https://orcid.org/0000-0002-5246-9391"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shparlinski, Igor E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.6958000063896179,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.6958000063896179,"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/T11166","display_name":"Analytic Number Theory Research","score":0.155799999833107,"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":0.07509999722242355,"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/polynomial-equations","display_name":"polynomial equations","score":0.7590000033378601},{"id":"https://openalex.org/keywords/finitely-generated-groups","display_name":"finitely generated groups","score":0.8840000033378601},{"id":"https://openalex.org/keywords/linear-recurrence-sequences","display_name":"linear recurrence sequences","score":0.8690000176429749},{"id":"https://openalex.org/keywords/number-of-solutions","display_name":"number of solutions","score":0.5210000276565552},{"id":"https://openalex.org/keywords/quadratic-equations","display_name":"quadratic equations","score":0.6690000295639038},{"id":"https://openalex.org/keywords/linear-equations","display_name":"linear equations","score":0.7710000276565552},{"id":"https://openalex.org/keywords/characteristic-zero","display_name":"characteristic zero","score":0.5170000195503235},{"id":"https://openalex.org/keywords/additive-combinatorics","display_name":"additive combinatorics","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8571000099182129},{"id":"https://openalex.org/C2781137444","wikidata":"https://www.wikidata.org/wiki/Q237105","display_name":"Sharpening","level":2,"score":0.6603000164031982},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5820000171661377},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.564300000667572},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.4821999967098236},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.41260001063346863},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3928999900817871},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3714999854564667},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.3292999863624573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3021000027656555},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2777000069618225},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07227","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07227","pdf_url":"https://arxiv.org/pdf/2610.07227","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.2610.07227","doi":"https://doi.org/10.48550/arxiv.2610.07227","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07227","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:2610.07227","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07227","pdf_url":"https://arxiv.org/pdf/2610.07227","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/W7220964100.pdf","grobid_xml":"https://content.openalex.org/works/W7220964100.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416112197","https://openalex.org/W7124417050","https://openalex.org/W2065854911","https://openalex.org/W1500541263","https://openalex.org/W4407281213","https://openalex.org/W2165906884","https://openalex.org/W7166316406","https://openalex.org/W1507584170","https://openalex.org/W2019586508","https://openalex.org/W571446603"],"abstract_inverted_index":{"We":[0,100],"obtain":[1,102],"new":[2],"and":[3,41,55,62,68,89,117],"essentially":[4],"optimal":[5],"bounds":[6,39],"on":[7],"the":[8,112],"number":[9],"of":[10,12,15,27,35,46,63,84,97,107,114],"solutions":[11],"diagonal":[13],"systems":[14],"$k$":[16],"polynomial":[17],"equations":[18,116],"in":[19,32,111],"$s$":[20],"variables":[21],"from":[22],"an":[23],"arbitrary":[24],"finite":[25],"subset":[26],"a":[28,33,82],"finitely":[29],"generated":[30],"group":[31],"field":[34],"characteristic":[36],"zero.":[37],"Our":[38],"generalise":[40],"sometimes":[42],"improve":[43],"previous":[44],"results":[45,104],"J.":[47],"Bourgain,":[48],"M.":[49],"Z.":[50],"Garaev,":[51],"S.":[52],"V.":[53],"Konyagin,":[54],"I.":[56,69,90],"E.":[57,70,91],"Shparlinski":[58,71,92],"(2014),":[59],"for":[60,73,105],"$k=1$,":[61],"A.":[64,66,85,87],"Manning,":[65,86],"Ostafe":[67,88],"(2026),":[72],"$k=2$.":[74],"In":[75],"turn,":[76],"this":[77],"improvement":[78],"leads":[79],"to":[80],"sharpening":[81],"result":[83],"(2026)":[93],"concerning":[94],"arithmetic":[95],"statistics":[96],"certain":[98],"matrices.":[99],"also":[101],"similar":[103],"$s$-tuples":[106],"linear":[108,115],"recurrence":[109],"sequences,":[110],"case":[113],"quadratic":[118],"equations.":[119]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
