{"id":"https://openalex.org/W7149533217","doi":"https://doi.org/10.1080/00255572.2026.2748847","title":"A Diophantine generalisation of Fourier's irrationality trick","display_name":"A Diophantine generalisation of Fourier's irrationality trick","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7149533217","doi":"https://doi.org/10.1080/00255572.2026.2748847"},"language":"en","primary_location":{"id":"doi:10.1080/00255572.2026.2748847","doi":"https://doi.org/10.1080/00255572.2026.2748847","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00255572.2026.2748847","pdf_url":null,"source":{"id":"https://openalex.org/S2764830807","display_name":"The Mathematical Gazette","issn_l":"0025-5572","issn":["0025-5572","2056-6328"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Mathematical Gazette","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/2610.40698","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121958423","display_name":"Archan Chattopadhyay","orcid":"https://orcid.org/0000-0003-4132-4688","observed_orcids":["https://orcid.org/0000-0003-4132-4688"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Archan Chattopadhyay","raw_affiliation_strings":["Howrah, West Bengal, India"],"raw_orcid":"https://orcid.org/0000-0003-4132-4688","affiliations":[{"raw_affiliation_string":"Howrah, West Bengal, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090745072","display_name":"Chandan Chattopadhyay","orcid":"https://orcid.org/0009-0008-0394-9146","observed_orcids":["https://orcid.org/0009-0008-0394-9146"]},"institutions":[{"id":"https://openalex.org/I4405271234","display_name":"Narasinha Dutt College","ror":"https://ror.org/023kqfv06","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405271234"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Chandan Chattopadhyay","raw_affiliation_strings":["Narasinha Dutt College"],"raw_orcid":"https://orcid.org/0009-0008-0394-9146","affiliations":[{"raw_affiliation_string":"Narasinha Dutt College","institution_ids":["https://openalex.org/I4405271234"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5121958423"],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32625561,"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":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9272000193595886,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9272000193595886,"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":0.04699999839067459,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.010900000110268593,"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/diophantine-approximation","display_name":"Diophantine approximation","score":0.8790000081062317},{"id":"https://openalex.org/keywords/continued-fractions","display_name":"continued fractions","score":0.7940000295639038},{"id":"https://openalex.org/keywords/linear-forms-in-logarithms","display_name":"linear forms in logarithms","score":0.5720000267028809}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6172000169754028},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.40849998593330383},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36070001125335693},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2669999897480011},{"id":"https://openalex.org/C2777019708","wikidata":"https://www.wikidata.org/wiki/Q1412340","display_name":"Irrationality","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2515999972820282}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00255572.2026.2748847","doi":"https://doi.org/10.1080/00255572.2026.2748847","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00255572.2026.2748847","pdf_url":null,"source":{"id":"https://openalex.org/S2764830807","display_name":"The Mathematical Gazette","issn_l":"0025-5572","issn":["0025-5572","2056-6328"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Mathematical Gazette","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2610.40698","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40698","pdf_url":"https://arxiv.org/pdf/2610.40698","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.2610.40698","doi":"https://doi.org/10.48550/arxiv.2610.40698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.40698","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"},{"id":"doi:10.13140/rg.2.2.32901.72165","doi":"https://doi.org/10.13140/rg.2.2.32901.72165","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.32901.72165","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.40698","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40698","pdf_url":"https://arxiv.org/pdf/2610.40698","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/W7149533217.pdf","grobid_xml":"https://content.openalex.org/works/W7149533217.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1605256314","https://openalex.org/W1978915576","https://openalex.org/W1988729425","https://openalex.org/W2022381665","https://openalex.org/W2329095032","https://openalex.org/W2334165056","https://openalex.org/W2335244159","https://openalex.org/W2337693832","https://openalex.org/W2945964015","https://openalex.org/W3092512459","https://openalex.org/W4239745146","https://openalex.org/W4243409352","https://openalex.org/W4248492559","https://openalex.org/W4292806204"],"related_works":["https://openalex.org/W7097766980","https://openalex.org/W3048671291","https://openalex.org/W2257236985","https://openalex.org/W7219802891","https://openalex.org/W4205305745","https://openalex.org/W2270876211","https://openalex.org/W820233093","https://openalex.org/W7098900888","https://openalex.org/W7127113516","https://openalex.org/W2797842094"],"abstract_inverted_index":{"We":[0],"revisit":[1],"Fourier's":[2],"method":[3],"for":[4],"proving":[5],"the":[6],"irrationality":[7,50],"of":[8,24],"e":[9],"and":[10,33],"generalise":[11],"it":[12],"into":[13],"a":[14,21,44,58],"unified":[15],"Diophantine":[16],"framework,":[17],"which":[18],"applies":[19],"to":[20],"broad":[22],"class":[23],"series":[25],"with":[26],"bounded":[27],"or":[28],"mildly":[29],"growing":[30],"integer":[31,39],"numerators,":[32],"suitably":[34],"growing,":[35],"divisible":[36],"denominators.":[37],"Using":[38],"linear":[40],"forms,":[41],"we":[42],"establish":[43],"general":[45],"criterion":[46],"that":[47],"recovers":[48],"classical":[49],"results":[51],"while":[52],"also":[53],"generating":[54],"new":[55],"ones":[56],"within":[57],"single":[59],"structural":[60],"approach.":[61]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-04-05T00:00:00"}