{"id":"https://openalex.org/W2962869498","doi":"https://doi.org/10.3390/sym11060754","title":"Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products","display_name":"Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products","publication_year":2019,"publication_date":"2019-06-04","ids":{"openalex":"https://openalex.org/W2962869498","doi":"https://doi.org/10.3390/sym11060754","mag":"2962869498"},"language":"en","primary_location":{"id":"doi:10.3390/sym11060754","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060754","pdf_url":"https://www.mdpi.com/2073-8994/11/6/754/pdf?version=1559639493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/6/754/pdf?version=1559639493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068279274","display_name":"A. C. L. Ashton","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"A. C. L. Ashton","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007372240","display_name":"A. S. Fokas","orcid":"https://orcid.org/0000-0002-5881-802X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. S. Fokas","raw_affiliation_strings":["Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2560, USA"],"affiliations":[{"raw_affiliation_string":"Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089-2560, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068279274"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4219,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80179616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"6","first_page":"754","last_page":"754"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9990000128746033,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9988999962806702,"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/riemann-zeta-function","display_name":"Riemann zeta function","score":0.7655825614929199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.615347683429718},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5888062119483948},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.549023449420929},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5109040141105652},{"id":"https://openalex.org/keywords/arithmetic-zeta-function","display_name":"Arithmetic zeta function","score":0.47575587034225464},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.44678935408592224},{"id":"https://openalex.org/keywords/functional-equation","display_name":"Functional equation","score":0.440807044506073},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.4172629117965698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3026426136493683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.129230797290802},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1043626070022583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05340409278869629}],"concepts":[{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.7655825614929199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.615347683429718},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5888062119483948},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.549023449420929},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5109040141105652},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.47575587034225464},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.44678935408592224},{"id":"https://openalex.org/C153576954","wikidata":"https://www.wikidata.org/wiki/Q594452","display_name":"Functional equation","level":3,"score":0.440807044506073},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4172629117965698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3026426136493683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.129230797290802},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1043626070022583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05340409278869629},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11060754","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060754","pdf_url":"https://www.mdpi.com/2073-8994/11/6/754/pdf?version=1559639493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:91566ce43718455fac49068d6940c051","is_oa":true,"landing_page_url":"https://doaj.org/article/91566ce43718455fac49068d6940c051","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 6, p 754 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11060754","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060754","pdf_url":"https://www.mdpi.com/2073-8994/11/6/754/pdf?version=1559639493","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4013382746","display_name":null,"funder_award_id":"EP/N006593/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962869498.pdf","grobid_xml":"https://content.openalex.org/works/W2962869498.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1592212038","https://openalex.org/W1641268399","https://openalex.org/W1969448553","https://openalex.org/W1976835067","https://openalex.org/W1982420169","https://openalex.org/W1995956091","https://openalex.org/W2024721763","https://openalex.org/W2072548119","https://openalex.org/W2073740002","https://openalex.org/W2106226212","https://openalex.org/W2775453794","https://openalex.org/W2972921032"],"related_works":["https://openalex.org/W1513480133","https://openalex.org/W4294651012","https://openalex.org/W2909634389","https://openalex.org/W2086661656","https://openalex.org/W4288019650","https://openalex.org/W3185914399","https://openalex.org/W2889263256","https://openalex.org/W2996016345","https://openalex.org/W4289676462","https://openalex.org/W2610184042"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"several":[3],"relations":[4,25,81],"are":[5],"obtained":[6],"among":[7],"the":[8,33,41,45,55,74,79,83,87,92],"Riemann":[9],"zeta":[10,13,47,95],"and":[11,38],"Hurwitz":[12,46,94],"functions,":[14],"as":[15,17],"well":[16],"their":[18],"products.":[19],"A":[20],"particular":[21],"case":[22],"of":[23,32,36,44,58,66,73,78,91],"these":[24],"give":[26],"rise":[27],"to":[28],"a":[29,50,59,64,70],"simple":[30],"re-derivation":[31],"important":[34],"results":[35],"Katsurada":[37],"Matsumoto":[39],"on":[40],"mean":[42],"square":[43],"function.":[48],"Also,":[49],"relation":[51],"derived":[52],"here":[53],"provides":[54],"starting":[56],"point":[57],"novel":[60],"approach":[61],"which,":[62],"in":[63],"series":[65],"companion":[67],"papers,":[68],"yields":[69],"formal":[71],"proof":[72],"Lindel\u00f6f":[75],"hypothesis.":[76],"Some":[77],"above":[80],"motivate":[82],"need":[84],"for":[85],"analysing":[86],"large":[88],"\u03b1":[89,102,109],"behaviour":[90],"modified":[93],"function":[96],"\u03b6":[97],"1":[98],"(":[99,111],"s":[100,105],",":[101,104,108,113,116],")":[103,115],"\u2208":[106,110],"C":[107],"0":[112],"\u221e":[114],"which":[117],"is":[118],"also":[119],"presented":[120],"here.":[121]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
