{"id":"https://openalex.org/W4403780252","doi":"https://doi.org/10.1080/10586458.2026.2742226","title":"Determinants of Mahler Measures and Special Values of L -Functions","display_name":"Determinants of Mahler Measures and Special Values of L -Functions","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W4403780252","doi":"https://doi.org/10.1080/10586458.2026.2742226"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2026.2742226","doi":"https://doi.org/10.1080/10586458.2026.2742226","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2026.2742226","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2409.14714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038056691","display_name":"Detchat Samart","orcid":"https://orcid.org/0000-0003-2486-2396","observed_orcids":["https://orcid.org/0000-0003-2486-2396"]},"institutions":[{"id":"https://openalex.org/I129488602","display_name":"Burapha University","ror":"https://ror.org/01ff74m36","country_code":"TH","type":"education","lineage":["https://openalex.org/I129488602"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Detchat Samart","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Burapha University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Burapha University","institution_ids":["https://openalex.org/I129488602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004745198","display_name":"Zhengyu Tao","orcid":"https://orcid.org/0000-0002-2884-6732","observed_orcids":["https://orcid.org/0000-0002-2884-6732"]},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengyu Tao","raw_affiliation_strings":["School of Mathematics, Hefei University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hefei University of Technology","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038056691"],"corresponding_institution_ids":["https://openalex.org/I129488602"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02405299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.5166000127792358,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.5166000127792358,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.361299991607666,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.05380000174045563,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mahler-measure","display_name":"Mahler measure","score":0.8880000114440918},{"id":"https://openalex.org/keywords/l-value","display_name":"L-values","score":0.6230000257492065},{"id":"https://openalex.org/keywords/cusp-forms","display_name":"cusp forms","score":0.8820000290870667},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"complex multiplication","score":0.7239999771118164},{"id":"https://openalex.org/keywords/cm-elliptic-curves","display_name":"CM elliptic curves","score":0.9269999861717224},{"id":"https://openalex.org/keywords/bivariate-polynomials","display_name":"bivariate polynomials","score":0.9539999961853027},{"id":"https://openalex.org/keywords/totally-real-number-fields","display_name":"totally real fields","score":0.8550000190734863},{"id":"https://openalex.org/keywords/galois-conjugates","display_name":"Galois conjugates","score":0.9010000228881836},{"id":"https://openalex.org/keywords/matrix-determinants","display_name":"matrix determinants","score":0.6919999718666077},{"id":"https://openalex.org/keywords/special-values-of-l-functions","display_name":"special values of L-functions","score":0.8640000224113464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4502449035644531},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.3870738446712494},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.38209372758865356}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2026.2742226","doi":"https://doi.org/10.1080/10586458.2026.2742226","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2026.2742226","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2409.14714","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2409.14714","pdf_url":"https://arxiv.org/pdf/2409.14714","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2409.14714","doi":"https://doi.org/10.48550/arxiv.2409.14714","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2409.14714","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:2409.14714","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2409.14714","pdf_url":"https://arxiv.org/pdf/2409.14714","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3916401050","display_name":null,"funder_award_id":"N41A640153","funder_id":"https://openalex.org/F4320322817","funder_display_name":"National Research Council of Thailand"}],"funders":[{"id":"https://openalex.org/F4320322817","display_name":"National Research Council of Thailand","ror":"https://ror.org/018wfhg78"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403780252.pdf","grobid_xml":"https://content.openalex.org/works/W4403780252.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W578225970","https://openalex.org/W1496632731","https://openalex.org/W1496801598","https://openalex.org/W1539383615","https://openalex.org/W1572759640","https://openalex.org/W1657113067","https://openalex.org/W1884403692","https://openalex.org/W1965220598","https://openalex.org/W1998754688","https://openalex.org/W2016094420","https://openalex.org/W2025384727","https://openalex.org/W2029988180","https://openalex.org/W2034354726","https://openalex.org/W2055944041","https://openalex.org/W2061257607","https://openalex.org/W2079886444","https://openalex.org/W2110093674","https://openalex.org/W2112102145","https://openalex.org/W2128765897","https://openalex.org/W2491759990","https://openalex.org/W2791465356","https://openalex.org/W2963833547","https://openalex.org/W3026017058","https://openalex.org/W3036381431","https://openalex.org/W3104603645","https://openalex.org/W3130884874","https://openalex.org/W4212885700","https://openalex.org/W4240694056","https://openalex.org/W4243943870","https://openalex.org/W4298185055","https://openalex.org/W4376863352","https://openalex.org/W4385606257","https://openalex.org/W4390784298","https://openalex.org/W4392764279"],"related_works":["https://openalex.org/W3104603645","https://openalex.org/W3021512892","https://openalex.org/W2016094420","https://openalex.org/W4298185055","https://openalex.org/W1998754688","https://openalex.org/W3087912279","https://openalex.org/W4392537651","https://openalex.org/W3006258651","https://openalex.org/W4392764279","https://openalex.org/W2762932858"],"abstract_inverted_index":{"We":[0],"consider":[1],"Mahler":[2,44,115],"measures":[3,45,116],"of":[4,8,28,48,50,62,67,86,93,109,126],"two":[5],"well-studied":[6],"families":[7],"bivariate":[9],"polynomials,":[10],"namely":[11],"Pt=x+x\u22121+y+y\u22121+t":[12],"and":[13,96],"Qt=x3+y3+1\u2212t3xy,":[14],"where":[15],"t":[16,63,87],"is":[17],"a":[18],"complex":[19,79],"parameter.":[20],"In":[21],"the":[22,25,74],"cases":[23],"when":[24],"zero":[26],"loci":[27],"these":[29],"polynomials":[30],"define":[31],"CM":[32],"elliptic":[33,76,100],"curves":[34,77,101],"over":[35],"number":[36,65,91],"fields,":[37],"we":[38,56,105],"derive":[39],"general":[40],"formulas":[41],"for":[42,72,82],"their":[43,119],"in":[46,64,88],"terms":[47],"L-values":[49],"cusp":[51],"forms.":[52],"For":[53],"each":[54],"family,":[55],"also":[57],"classify":[58],"all":[59,83],"possible":[60],"values":[61,85],"fields":[66,92],"degree":[68,94],"not":[69],"exceeding":[70],"4":[71],"which":[73],"corresponding":[75,98,117],"have":[78],"multiplication.":[80],"Finally,":[81],"such":[84],"totally":[89],"real":[90],"n=2":[95],"n=4,":[97],"to":[99,118],"Ft":[102],"(resp.":[103,128],"Ct),":[104],"prove":[106],"that":[107],"determinants":[108],"n\u00d7n":[110],"matrices":[111],"whose":[112],"entries":[113],"are":[114,122],"Galois":[120],"conjugates":[121],"non-zero":[123],"rational":[124],"multiples":[125],"L(n)(Ft,0)":[127],"L(n)(Ct,0)).":[129]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-10-26T00:00:00"}