{"id":"https://openalex.org/W4392678249","doi":"https://doi.org/10.1016/j.ffa.2026.102834","title":"Distribution of solutions to systems of congruences in balls","display_name":"Distribution of solutions to systems of congruences in balls","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W4392678249","doi":"https://doi.org/10.1016/j.ffa.2026.102834"},"language":"en","primary_location":{"id":"doi:10.1016/j.ffa.2026.102834","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ffa.2026.102834","pdf_url":null,"source":{"id":"https://openalex.org/S925225069","display_name":"Finite Fields and Their Applications","issn_l":"1071-5797","issn":["1071-5797","1090-2465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finite Fields and Their Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.ffa.2026.102834","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094123549","display_name":"Michael Harm","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Harm","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0001-5862-0646","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5094123549"],"corresponding_institution_ids":[],"apc_list":{"value":2530,"currency":"USD","value_usd":2530},"apc_paid":{"value":2530,"currency":"USD","value_usd":2530},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01088224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"113","issue":null,"first_page":"102834","last_page":"102834"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.7775999903678894,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.7775999903678894,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.8628122806549072},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.6096950769424438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42164599895477295},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25481945276260376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17882448434829712}],"concepts":[{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.8628122806549072},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.6096950769424438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42164599895477295},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25481945276260376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17882448434829712}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.ffa.2026.102834","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ffa.2026.102834","pdf_url":null,"source":{"id":"https://openalex.org/S925225069","display_name":"Finite Fields and Their Applications","issn_l":"1071-5797","issn":["1071-5797","1090-2465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finite Fields and Their Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2403.05078","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.05078","pdf_url":"https://arxiv.org/pdf/2403.05078","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,"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"},{"id":"pmh:oai:arXiv.org:2403.05078","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2403.05078","pdf_url":"https://arxiv.org/pdf/2403.05078","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,"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.2403.05078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2403.05078","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,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1016/j.ffa.2026.102834","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ffa.2026.102834","pdf_url":null,"source":{"id":"https://openalex.org/S925225069","display_name":"Finite Fields and Their Applications","issn_l":"1071-5797","issn":["1071-5797","1090-2465"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Finite Fields and Their Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2778946875","https://openalex.org/W2023974151","https://openalex.org/W2163207601","https://openalex.org/W4301322097","https://openalex.org/W2103827354","https://openalex.org/W2590546754","https://openalex.org/W4293173044","https://openalex.org/W2472631239","https://openalex.org/W2964315014","https://openalex.org/W3049627489"],"abstract_inverted_index":{"Let":[0],"$G_1,\\dots,":[1],"G_n\\in":[2],"\\mathbb{F}_p[X_1,\\dots,X_m]$":[3],"be":[4],"$n$":[5],"polynomials":[6],"in":[7],"$m$":[8],"variables":[9],"over":[10],"the":[11,28,33,45,48,70],"finite":[12],"field":[13],"$\\mathbb{F}_p$":[14],"of":[15,37,47,64],"$p$":[16,23],"elements.":[17],"For":[18],"any":[19],"sufficiently":[20],"large":[21],"prime":[22],"and":[24,73],"non-trivial":[25,34],"bounds":[26,68],"for":[27,69],"Weyl":[29],"sums":[30],"associated":[31],"to":[32],"linear":[35],"combinations":[36],"$G=(G_1,\\dots,":[38],"G_n)$,":[39],"we":[40],"study":[41],"various":[42],"properties":[43],"regarding":[44],"distribution":[46],"vectors":[49],"by":[50],"fractional":[51],"parts":[52],"\\begin{equation*}":[53],"\\bigg(\\bigg\\{":[54],"\\frac{G_1(\\textbf{x})}{p}\\bigg\\},\\cdots,\\bigg\\{":[55],"\\frac{G_n(\\textbf{x})}{p}\\bigg\\}\\bigg)\\in":[56],"\\mathbb{T}^n,\\hspace{10pt}":[57],"\\textbf{x}\\in":[58],"\\mathbb{F}_p^m.":[59],"\\end{equation*}":[60],"We":[61],"prove":[62],"refinements":[63],"equidistribution,":[65],"such":[66],"as":[67],"ball":[71],"discrepancy":[72],"variance.":[74]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2024-03-13T00:00:00"}
