{"id":"https://openalex.org/W2080716897","doi":"https://doi.org/10.1080/10586458.2005.10128901","title":"The Asymptotic Distribution of Exponential Sums, II","display_name":"The Asymptotic Distribution of Exponential Sums, II","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2080716897","doi":"https://doi.org/10.1080/10586458.2005.10128901","mag":"2080716897"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2005.10128901","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128901","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,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108779337","display_name":"S. J. Patterson","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"S. J. Patterson","raw_affiliation_strings":["Mathematisches Institut, Bunsenstr. 3-5, 37073 G\u00f6ttingen, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Bunsenstr. 3-5, 37073 G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108779337"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":null,"apc_paid":null,"fwci":1.113,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75387046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"1","first_page":"87","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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":1.0,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.9274642467498779},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8403521180152893},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6178222894668579},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6170480251312256},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5244467854499817},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48259031772613525},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.41206058859825134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41017404198646545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33819133043289185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2636745572090149}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9274642467498779},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8403521180152893},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6178222894668579},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6170480251312256},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5244467854499817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48259031772613525},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.41206058859825134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41017404198646545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33819133043289185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2636745572090149}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2005.10128901","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128901","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,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"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:CULeuclid:euclid.em/1120145573","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1120145573","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W62569548","https://openalex.org/W605079440","https://openalex.org/W615705420","https://openalex.org/W622723035","https://openalex.org/W971622133","https://openalex.org/W1512374421","https://openalex.org/W1620449130","https://openalex.org/W1967878303","https://openalex.org/W1973039890","https://openalex.org/W1981479929","https://openalex.org/W1988085365","https://openalex.org/W2001328799","https://openalex.org/W2016431841","https://openalex.org/W2024791221","https://openalex.org/W2026290737","https://openalex.org/W2058324165","https://openalex.org/W2059946380","https://openalex.org/W2061107511","https://openalex.org/W2081163625","https://openalex.org/W2081338783","https://openalex.org/W2110383145","https://openalex.org/W2123628410","https://openalex.org/W2132248880","https://openalex.org/W2132684431","https://openalex.org/W2138932858","https://openalex.org/W2323125905","https://openalex.org/W2497424908","https://openalex.org/W2566928873","https://openalex.org/W2734781561"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W2351051352","https://openalex.org/W2089990214"],"abstract_inverted_index":{"Let":[0],"\u0192(x)":[1,32],"be":[2],"a":[3,15,40,48],"polynomial":[4,17],"with":[5],"integral":[6],"coefficients":[7],"and":[8,38],"let,":[9],"for":[10,43],".":[11,23],"If":[12],"\u0192":[13],"is":[14,20],"cubic":[16],"then":[18],"it":[19],"expected":[21],"that":[22],"In":[24],"this":[25],"paper,":[26],"we":[27],"consider":[28],"the":[29,52],"special":[30],"case":[31],"=":[33],"Ax":[34],"3":[35],"+":[36],"Bx":[37],"propose":[39],"precise":[41],"formula":[42],"k(\u0192).":[44],"This":[45],"conjecture":[46],"represents":[47],"refined":[49],"version":[50],"of":[51],"classical":[53],"Kummer":[54],"conjecture.":[55]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}