{"id":"https://openalex.org/W7225569676","doi":"https://doi.org/10.5281/zenodo.24054093","title":"Exact Gram Inversion for Fractional-Part Approximation","display_name":"Exact Gram Inversion for Fractional-Part Approximation","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225569676","doi":"https://doi.org/10.5281/zenodo.24054093"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24054093","doi":"https://doi.org/10.5281/zenodo.24054093","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24054093","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066869492","display_name":"Deep Bhattacharjee","orcid":"https://orcid.org/0000-0003-0466-750X","observed_orcids":["https://orcid.org/0000-0003-0466-750X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhattacharjee, Deep","raw_affiliation_strings":["Electro-Gravitational Space Propulsion Laboratory (EGSPL), India"],"raw_orcid":"https://orcid.org/0000-0003-0466-750X","affiliations":[{"raw_affiliation_string":"Electro-Gravitational Space Propulsion Laboratory (EGSPL), India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125176234","display_name":"Pallab Nandi","orcid":"https://orcid.org/0009-0002-4221-339X","observed_orcids":["https://orcid.org/0009-0002-4221-339X"]},"institutions":[{"id":"https://openalex.org/I127439422","display_name":"Indian Institute of Science Education and Research Kolkata","ror":"https://ror.org/00djv2c17","country_code":"IN","type":"education","lineage":["https://openalex.org/I127439422"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nandi, Pallab","raw_affiliation_strings":["Former student, Indian Institute of Science Education and Research Kolkata, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Former student, Indian Institute of Science Education and Research Kolkata, India","institution_ids":["https://openalex.org/I127439422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037361314","display_name":"Onwuka Frederick","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I13144388","display_name":"Ekiti State University","ror":"https://ror.org/02c4zkr79","country_code":"NG","type":"education","lineage":["https://openalex.org/I13144388"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Frederick, Onwuka","raw_affiliation_strings":["Ekiti State University, Ado-Ekiti, Nigeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ekiti State University, Ado-Ekiti, Nigeria","institution_ids":["https://openalex.org/I13144388"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086674134","display_name":"Priyanka Samal","orcid":"https://orcid.org/0000-0002-2343-9169","observed_orcids":["https://orcid.org/0000-0002-2343-9169"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Samal, Priyanka","raw_affiliation_strings":["Independent researcher, India"],"raw_orcid":"https://orcid.org/0000-0002-2343-9169","affiliations":[{"raw_affiliation_string":"Independent researcher, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9907000064849854,"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":0.9907000064849854,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/least-squares-error","display_name":"least squares error","score":0.7149999737739563},{"id":"https://openalex.org/keywords/hardy-spaces","display_name":"Hardy spaces","score":0.625},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.8100000023841858}],"concepts":[{"id":"https://openalex.org/C148837635","wikidata":"https://www.wikidata.org/wiki/Q1742397","display_name":"Sawtooth wave","level":2,"score":0.8920000195503235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7730000019073486},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5439000129699707},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5332000255584717},{"id":"https://openalex.org/C161369605","wikidata":"https://www.wikidata.org/wiki/Q41803","display_name":"Gram","level":3,"score":0.5292999744415283},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5117999911308289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46149998903274536},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.27889999747276306}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24054093","doi":"https://doi.org/10.5281/zenodo.24054093","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.24054094","doi":"https://doi.org/10.5281/zenodo.24054094","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054094","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.24054105","doi":"https://doi.org/10.5281/zenodo.24054105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24054093","doi":"https://doi.org/10.5281/zenodo.24054093","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7161576659","https://openalex.org/W7204015783","https://openalex.org/W7153870318","https://openalex.org/W2766373213","https://openalex.org/W7221644892","https://openalex.org/W2062488030","https://openalex.org/W7103650754","https://openalex.org/W7134951720","https://openalex.org/W7117296126","https://openalex.org/W7203500145"],"abstract_inverted_index":{"Exact":[0],"finite":[1,26],"Gram":[2,35,53],"inversion,":[3],"ordinary":[4,30],"sawtooth":[5,31],"least-squares":[6,27],"errors":[7],"and":[8,15,37,42,58],"rigorous":[9,55],"reciprocal-dilate":[10,48],"certificates.":[11],"The":[12,62],"Riemann":[13,63],"hypothesis":[14,64],"the":[16,25,46],"limiting":[17],"reciprocal":[18],"approximation":[19],"criterion":[20],"remain":[21],"unproved.":[22],"We":[23],"solve":[24],"problem":[28],"for":[29],"dilates":[32],"by":[33],"explicit":[34],"inversion":[36],"obtain":[38],"its":[39],"exact":[40],"error":[41],"asymptotic":[43],"constant.":[44],"For":[45],"distinct":[47],"problem,":[49],"we":[50],"derive":[51],"rational":[52],"certificates,":[54],"residual":[56],"intervals":[57],"Hardy-space":[59],"zero":[60],"bounds.":[61],"remains":[65],"open.":[66]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}