{"id":"https://openalex.org/W2010512871","doi":"https://doi.org/10.1090/s0025-5718-2013-02778-0","title":"On some Diophantine systems involving symmetric polynomials","display_name":"On some Diophantine systems involving symmetric polynomials","publication_year":2013,"publication_date":"2013-10-22","ids":{"openalex":"https://openalex.org/W2010512871","doi":"https://doi.org/10.1090/s0025-5718-2013-02778-0","mag":"2010512871"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02778-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02778-0","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2013-02778-0/S0025-5718-2013-02778-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2013-02778-0/S0025-5718-2013-02778-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005743799","display_name":"Maciej Ulas","orcid":"https://orcid.org/0000-0002-1927-4453"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Maciej Ulas","raw_affiliation_strings":["Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, \u00c5\u0081ojasiewicza 6, 30 - 348 Krak\u00c3\u00b3w, Poland","Jagiellonian University Faculty of Mathematics and Computer Science Institute of Mathematics \u0141ojasiewicza 6 30-348 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, \u00c5\u0081ojasiewicza 6, 30 - 348 Krak\u00c3\u00b3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Jagiellonian University Faculty of Mathematics and Computer Science Institute of Mathematics \u0141ojasiewicza 6 30-348 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005743799"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":2.2388,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86434641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"83","issue":"288","first_page":"1915","last_page":"1930"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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":0.9997000098228455,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9957000017166138,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4353957772254944},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22864994406700134}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4353957772254944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22864994406700134}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02778-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02778-0","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2013-02778-0/S0025-5718-2013-02778-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.743.3563","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.743.3563","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/1305.6237.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2013-02778-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02778-0","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2013-02778-0/S0025-5718-2013-02778-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2010512871.pdf","grobid_xml":"https://content.openalex.org/works/W2010512871.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W16785173","https://openalex.org/W1486898453","https://openalex.org/W1555475515","https://openalex.org/W1988671481","https://openalex.org/W2093006084","https://openalex.org/W2329845704","https://openalex.org/W2798483379","https://openalex.org/W4206503652"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,175,216,240,260],"content-type=\"math/mathml\">":[2,176,217,241,261,290],"<mml:math":[3,177,218,242,262,291],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,178,219,243,263,292],"alttext=\"sigma":[5,293],"Subscript":[6,16,34,41,47,50,302,310,320],"i":[7,35],"Baseline":[8,18,36,44,304,312,322],"left-parenthesis":[9,295,313],"x":[10,15,40,46,296,301,314,319],"1":[11,23,26,43,294,297,315],"comma":[12,14,245,298,300,308,316,318],"ellipsis":[13,31,45,299,317],"n":[17,38,303,311,321],"right-parenthesis":[19,305,323],"equals":[20,306,324],"sigma-summation":[21],"Underscript":[22],"less-than-or-equal-to":[24,37],"k":[25,28,33,42,48],"greater-than":[27,30,32],"2":[29],"Endscripts":[39],"Sub":[49],"i\">":[51],"<mml:semantics>":[52,180,223,247,268,327],"<mml:mrow>":[53,224,248,269,328],"<mml:msub>":[54,65,77,97,105,117,130,134,146,150,329,340,352],"<mml:mi>":[55,330],"\u03c3":[56,331],"</mml:mi>":[57,332],"<mml:mrow":[58,67,79,91,99,107,119,132,136,148,152,333,342],"class=\"MJX-TeXAtom-ORD\">":[59,68,80,92,100,108,120,133,137,149,153,334,343],"<mml:mi>i</mml:mi>":[60,121,154,181],"</mml:mrow>":[61,70,82,102,110,122,128,139,141,155,157,159,230,252,276,336,345],"</mml:msub>":[62,71,83,103,111,123,140,142,156,158,337,346],"<mml:mo":[63,84,338],"stretchy=\"false\">(</mml:mo>":[64,339],"<mml:mi>x</mml:mi>":[66,78,131,147,341,353],"<mml:mn>1</mml:mn>":[69,93,101,138,335,344],"<mml:mo>,</mml:mo>":[72,76,250,347,351],"<mml:mo>":[73,88,94,113,124,143,226,272,348],"\u2026":[74,114,144,349],"</mml:mo>":[75,90,96,115,126,145,228,274,350],"<mml:mi>n</mml:mi>":[81,127,225],"stretchy=\"false\">)</mml:mo>":[85],"<mml:mo>=</mml:mo>":[86],"<mml:munder>":[87],"\u2211":[89],"\u2264":[95,125],"<mml:mi>k</mml:mi>":[98,106,118,135,151],"<mml:mo>&gt;</mml:mo>":[104,112,116],"<mml:mn>2</mml:mn>":[109],"</mml:munder>":[129],"<mml:annotation":[160,182,231,253,277],"encoding=\"application/x-tex\">\\sigma":[161],"_{i}(x_{1},\\ldots":[162],",":[163,283],"x_{n})=\\sum":[164],"_{1\\leq":[165],"k_{1}&gt;k_{2}&gt;\\ldots":[166],"&gt;k_{i}\\leq":[167],"n}x_{k_{1}}\\ldots":[168],"x_{k_{i}}</mml:annotation>":[169],"</mml:semantics>":[170,184,234,256,280],"</mml:math>":[171,185,235,257,281],"</inline-formula>":[172,186,236,258,282],"be":[173],"the":[174,198,284],"alttext=\"i\">":[179],"encoding=\"application/x-tex\">i</mml:annotation>":[183],"-th":[187],"elementary":[188],"symmetric":[189],"polynomial.":[190],"In":[191],"this":[192],"note":[193],"we":[194,211],"generalize":[195],"and":[196,207,237],"extend":[197],"results":[199],"obtained":[200],"in":[201],"a":[202,307],"recent":[203],"work":[204],"of":[205,286],"Zhang":[206],"Cai.":[208],"More":[209],"precisely,":[210],"prove":[212],"that":[213],"for":[214],"each":[215],"alttext=\"n":[220],"greater-than-or-equal-to":[221],"4\">":[222],"\u2265":[227],"<mml:mn>4</mml:mn>":[229],"encoding=\"application/x-tex\">n\\geq":[232],"4</mml:annotation>":[233],"rational":[238],"numbers":[239],"alttext=\"a":[244,264],"b\">":[246],"<mml:mi>a</mml:mi>":[249,270],"<mml:mi>b</mml:mi>":[251,271],"encoding=\"application/x-tex\">a,":[254],"b</mml:annotation>":[255],"with":[259],"b":[265,325],"not-equals":[266],"0\">":[267],"\u2260":[273],"<mml:mn>0</mml:mn>":[275],"encoding=\"application/x-tex\">ab\\neq":[278],"0</mml:annotation>":[279],"system":[285],"diophantine":[287],"equations":[288],"<disp-formula":[289],"sigma":[309],"comma\">":[326]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
