{"id":"https://openalex.org/W1978527887","doi":"https://doi.org/10.1137/120886418","title":"On New Sum-Product--Type Estimates","display_name":"On New Sum-Product--Type Estimates","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1978527887","doi":"https://doi.org/10.1137/120886418","mag":"1978527887"},"language":"en","primary_location":{"id":"doi:10.1137/120886418","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120886418","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1207.6785","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087367773","display_name":"Serge\u012d Konyagin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sergei V. Konyagin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113807649","display_name":"Misha Rudnev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Misha Rudnev","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087367773"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3293,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84748083,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"2","first_page":"973","last_page":"990"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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":0.9934999942779541,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9836999773979187,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7045527696609497},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6640924215316772},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6579036116600037},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5745791792869568},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5410131216049194},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5393850803375244},{"id":"https://openalex.org/keywords/product-type","display_name":"Product type","score":0.4377453327178955},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38851994276046753},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14146128296852112},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.046841055154800415}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7045527696609497},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6640924215316772},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6579036116600037},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5745791792869568},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5410131216049194},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5393850803375244},{"id":"https://openalex.org/C23219732","wikidata":"https://www.wikidata.org/wiki/Q7247800","display_name":"Product type","level":2,"score":0.4377453327178955},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38851994276046753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14146128296852112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.046841055154800415},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/120886418","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120886418","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1207.6785","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1207.6785","pdf_url":"https://arxiv.org/pdf/1207.6785","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/21cdc415-c13f-46e9-98fc-e2727dff639f","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/21cdc415-c13f-46e9-98fc-e2727dff639f","pdf_url":"https://research-information.bris.ac.uk/ws/files/96434595/120886418.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Konyagin, SV & Rudnev, M 2013, 'On new sum-product-type estimates', SIAM Journal on Discrete Mathematics, vol. 27, no. 2, pp. 973\u2013990. https://doi.org/10.1137/120886418","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"mag:1978527887","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1207.6785.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.749.7606","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.749.7606","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1207.6785.pdf","raw_type":"text"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/21cdc415-c13f-46e9-98fc-e2727dff639f","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/21cdc415-c13f-46e9-98fc-e2727dff639f","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Konyagin, SV & Rudnev, M 2013, 'On new sum-product-type estimates', SIAM Journal on Discrete Mathematics, vol. 27, no. 2, pp. 973\u2013990. https://doi.org/10.1137/120886418","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1207.6785","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1207.6785","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:oai:arXiv.org:1207.6785","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1207.6785","pdf_url":"https://arxiv.org/pdf/1207.6785","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.550000011920929,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1572478586","https://openalex.org/W1579814185","https://openalex.org/W1585722514","https://openalex.org/W1976075351","https://openalex.org/W1992758844","https://openalex.org/W1998666916","https://openalex.org/W2029408549","https://openalex.org/W2075616478","https://openalex.org/W2086861401","https://openalex.org/W2103381743","https://openalex.org/W2108616329","https://openalex.org/W2129684959","https://openalex.org/W2166961358","https://openalex.org/W2167472711","https://openalex.org/W2963747036","https://openalex.org/W2963769834"],"related_works":["https://openalex.org/W2963887948","https://openalex.org/W2963755674","https://openalex.org/W2259973370","https://openalex.org/W2084859889","https://openalex.org/W2373664775","https://openalex.org/W2913206649","https://openalex.org/W3101283546","https://openalex.org/W2045903475","https://openalex.org/W2066153629","https://openalex.org/W3117051115","https://openalex.org/W2338643701","https://openalex.org/W3098480508","https://openalex.org/W2241408687","https://openalex.org/W2522969181","https://openalex.org/W2952429110","https://openalex.org/W3125417438","https://openalex.org/W2971201662","https://openalex.org/W201378979","https://openalex.org/W1754706138","https://openalex.org/W1966777587"],"abstract_inverted_index":{"New":[0],"lower":[1],"bounds":[2,49],"involving":[3,20,50],"sum,":[4],"difference,":[5],"product,":[6],"and":[7,37,68],"ratio":[8],"sets":[9],"of":[10,73],"a":[11],"set":[12,23,53],"$A\\subset":[13],"{\\mathbb":[14],"C}$":[15],"are":[16,38],"given.":[17],"The":[18,48],"estimates":[19],"the":[21,28,35,45,51,55,66,75],"sum":[22],"match,":[24],"up":[25],"to":[26,44,62],"constants,":[27],"state-of-the-art":[29],"estimates,":[30],"proven":[31],"by":[32,40,71],"Solymosi":[33],"for":[34],"reals":[36],"obtained":[39],"generalizing":[41],"his":[42],"approach":[43],"complex":[46,69],"plane.":[47],"difference":[52],"improve":[54],"currently":[56],"best":[57],"known":[58],"ones,":[59],"also":[60],"due":[61],"Solymosi,":[63],"in":[64],"both":[65],"real":[67],"cases":[70],"means":[72],"combining":[74],"Szemer\u00e9di--Trotter":[76],"theorem":[77],"with":[78],"an":[79],"arithmetic":[80],"combinatorics":[81],"technique.":[82]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}