{"id":"https://openalex.org/W3045272728","doi":"https://doi.org/10.13130/battistoni-francesco_phd2020-01-28","title":"APPLICATIONS OF PRIME DENSITIES IN NUMBER THEORY AND CLASSIFICATION OF NUMBER FIELDS WITH BOUNDED INVARIANTS","display_name":"APPLICATIONS OF PRIME DENSITIES IN NUMBER THEORY AND CLASSIFICATION OF NUMBER FIELDS WITH BOUNDED INVARIANTS","publication_year":2020,"publication_date":"2020-01-28","ids":{"openalex":"https://openalex.org/W3045272728","doi":"https://doi.org/10.13130/battistoni-francesco_phd2020-01-28","mag":"3045272728"},"language":"en","primary_location":{"id":"pmh:oai:air.unimi.it:2434/703505","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/703505","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2434/703505","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078659091","display_name":"Francesco Battistoni","orcid":"https://orcid.org/0000-0003-2119-1881"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"BATTISTONI, FRANCESCO","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2119-1881","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078659091"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12299305,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.58160001039505,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.58160001039505,"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/bounded-function","display_name":"Bounded function","score":0.7209169864654541},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.568636417388916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.544350802898407},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.4660191535949707},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.41915634274482727},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4089381694793701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3339640200138092},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32388532161712646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30746257305145264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09701898694038391}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7209169864654541},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.568636417388916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.544350802898407},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.4660191535949707},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.41915634274482727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4089381694793701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3339640200138092},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32388532161712646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30746257305145264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09701898694038391}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:air.unimi.it:2434/703505","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/703505","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},{"id":"doi:10.13130/battistoni-francesco_phd2020-01-28","is_oa":true,"landing_page_url":"https://doi.org/10.13130/battistoni-francesco_phd2020-01-28","pdf_url":null,"source":{"id":"https://openalex.org/S7407050996","display_name":"Universit\u00e0 degli Studi di Milano","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"},{"id":"mag:3045272728","is_oa":false,"landing_page_url":"https://air.unimi.it/bitstream/2434/703505/2/phd_unimi_R11763.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:air.unimi.it:2434/703505","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/703505","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/doctoralThesis"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2611599426","https://openalex.org/W2937648487","https://openalex.org/W2025235724","https://openalex.org/W948600717","https://openalex.org/W596752162","https://openalex.org/W2086505264","https://openalex.org/W1018587192","https://openalex.org/W2743875977","https://openalex.org/W2954277649","https://openalex.org/W773789010","https://openalex.org/W987980654","https://openalex.org/W2753813017","https://openalex.org/W2520070153","https://openalex.org/W2946497148","https://openalex.org/W3034953559","https://openalex.org/W2243724589","https://openalex.org/W2900513953","https://openalex.org/W2058964423","https://openalex.org/W2301591118","https://openalex.org/W2492536565"],"abstract_inverted_index":{"This":[0],"Ph.D.":[1],"thesis":[2],"collects":[3],"the":[4,28,34,40,45,57,60,72,77,85,88,101],"author's":[5],"works":[6],"and":[7,74,87,96,104],"interests":[8],"in":[9,33,53],"several":[10],"parts":[11],"of":[12,30,36,42,47,59,63,66,76,80,93],"Number":[13],"Theory,":[14],"from":[15],"algebraic":[16],"problems":[17],"related":[18],"to":[19,39,56],"relations":[20],"between":[21],"number":[22,54,82],"fields":[23,55],"which":[24],"are":[25],"based":[26],"on":[27,100,106],"factorization":[29],"prime":[31],"numbers":[32],"rings":[35],"integers,":[37],"up":[38],"application":[41],"tools":[43,103],"concerning":[44],"density":[46],"primes":[48],"with":[49,71],"given":[50],"splitting":[51],"type":[52],"computation":[58],"average":[61],"rank":[62],"specific":[64],"families":[65],"elliptic":[67],"curves,":[68],"concluding":[69],"finally":[70],"classification":[73],"estimate":[75],"main":[78],"invariants":[79],"a":[81],"field,":[83],"like":[84,111],"discriminant":[86],"regulator,":[89],"pursued":[90],"by":[91],"means":[92],"analytic":[94],"formulas":[95],"algorithmic":[97],"methods":[98],"developed":[99],"previous":[102],"implemented":[105],"suitable":[107],"computer":[108],"algebra":[109],"systems,":[110],"PARI/GP.":[112]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2020-07-29T00:00:00"}
