Publication Information

{'id': 'https://openalex.org/W3208033647', 'doi': None, 'title': 'A note on the exponential sums of the localized divisor functions', 'display_name': 'A note on the exponential sums of the localized divisor functions', 'publication_year': 2015, 'publication_date': '2015-12-01', 'ids': {'openalex': 'https://openalex.org/W3208033647', 'mag': '3208033647'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://ui.adsabs.harvard.edu/abs/2015arXiv151201128C/abstract', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5038203337', 'display_name': 'Giovanni Coppola', 'orcid': 'https://orcid.org/0000-0003-2548-7719'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Giovanni Coppola', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5034455809', 'display_name': 'Maurizio Laporta', 'orcid': 'https://orcid.org/0000-0001-5091-8491'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Maurizio Laporta', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 66}, 'biblio': {'volume': None, 'issue': None, 'first_page': '25', 'last_page': '28'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11166', 'display_name': 'Analytic Number Theory Research', 'score': 0.9998, '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': 0.9998, '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/T11329', 'display_name': 'Limits and Structures in Graph Theory', 'score': 0.9899, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, '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': 0.9857, '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/divisor-function', 'display_name': 'Divisor function', 'score': 0.65927964}, {'id': 'https://openalex.org/keywords/greatest-common-divisor', 'display_name': 'Greatest common divisor', 'score': 0.4854396}, {'id': 'https://openalex.org/keywords/multiple', 'display_name': 'Multiple', 'score': 0.46169648}, {'id': 'https://openalex.org/keywords/exponential-sum', 'display_name': 'Exponential sum', 'score': 0.4515792}], 'concepts': [{'id': 'https://openalex.org/C203492994', 'wikidata': 'https://www.wikidata.org/wiki/Q909669', 'display_name': 'Divisor (algebraic geometry)', 'level': 2, 'score': 0.8760098}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8004208}, {'id': 'https://openalex.org/C151376022', 'wikidata': 'https://www.wikidata.org/wiki/Q168698', 'display_name': 'Exponential function', 'level': 2, 'score': 0.73487383}, {'id': 'https://openalex.org/C97137487', 'wikidata': 'https://www.wikidata.org/wiki/Q729138', 'display_name': 'Integer (computer science)', 'level': 2, 'score': 0.72918165}, {'id': 'https://openalex.org/C67056277', 'wikidata': 'https://www.wikidata.org/wiki/Q915474', 'display_name': 'Divisor function', 'level': 3, 'score': 0.65927964}, {'id': 'https://openalex.org/C14036430', 'wikidata': 'https://www.wikidata.org/wiki/Q3736076', 'display_name': 'Function (biology)', 'level': 2, 'score': 0.65326947}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.63942736}, {'id': 'https://openalex.org/C2778067643', 'wikidata': 'https://www.wikidata.org/wiki/Q166507', 'display_name': 'Interval (graph theory)', 'level': 2, 'score': 0.55227065}, {'id': 'https://openalex.org/C125257309', 'wikidata': 'https://www.wikidata.org/wiki/Q131752', 'display_name': 'Greatest common divisor', 'level': 2, 'score': 0.4854396}, {'id': 'https://openalex.org/C90673727', 'wikidata': 'https://www.wikidata.org/wiki/Q901718', 'display_name': 'Product (mathematics)', 'level': 2, 'score': 0.46420604}, {'id': 'https://openalex.org/C164680029', 'wikidata': 'https://www.wikidata.org/wiki/Q1055293', 'display_name': 'Multiple', 'level': 2, 'score': 0.46169648}, {'id': 'https://openalex.org/C53638454', 'wikidata': 'https://www.wikidata.org/wiki/Q4446020', 'display_name': 'Exponential sum', 'level': 3, 'score': 0.4515792}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.45153362}, {'id': 'https://openalex.org/C77553402', 'wikidata': 'https://www.wikidata.org/wiki/Q13222579', 'display_name': 'Upper and lower bounds', 'level': 2, 'score': 0.43647754}, {'id': 'https://openalex.org/C204911207', 'wikidata': 'https://www.wikidata.org/wiki/Q860609', 'display_name': 'Generating function', 'level': 2, 'score': 0.418217}, {'id': 'https://openalex.org/C94375191', 'wikidata': 'https://www.wikidata.org/wiki/Q11205', 'display_name': 'Arithmetic', 'level': 1, 'score': 0.24540967}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.1343328}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.061498493}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C78458016', 'wikidata': 'https://www.wikidata.org/wiki/Q840400', 'display_name': 'Evolutionary biology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C86803240', 'wikidata': 'https://www.wikidata.org/wiki/Q420', 'display_name': 'Biology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://ui.adsabs.harvard.edu/abs/2015arXiv151201128C/abstract', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W3139234398', 'https://openalex.org/W3098164614', 'https://openalex.org/W2963745718', 'https://openalex.org/W2963524379', 'https://openalex.org/W2963388961', 'https://openalex.org/W2953390324', 'https://openalex.org/W2953162326', 'https://openalex.org/W2952180736', 'https://openalex.org/W2946044024', 'https://openalex.org/W2918170208', 'https://openalex.org/W2886485154', 'https://openalex.org/W2805336665', 'https://openalex.org/W2765622810', 'https://openalex.org/W2315032619', 'https://openalex.org/W2185755918', 'https://openalex.org/W2061626506', 'https://openalex.org/W2052631176', 'https://openalex.org/W1987133873', 'https://openalex.org/W1761371075', 'https://openalex.org/W1450293266'], 'abstract_inverted_index': {'We': [0], 'prove': [1], 'an': [2, 50], 'upper': [3], 'bound': [4], 'for': [5, 52, 56], 'the': [6, 16, 20, 53, 57], 'exponential': [7, 54], 'sum': [8, 55], 'associated': [9], 'to': [10, 24, 42], 'a': [11, 26, 31, 43], 'localized': [12], '$k-$divisor': [13, 58], 'function,': [14, 59], 'i.e.,': [15], 'counting': [17], 'function': [18], 'of': [19, 22, 33, 39], 'number': [21], 'ways': [23], 'write': [25], 'positive': [27, 36], 'integer': [28], '$n$': [29], 'as': [30], 'product': [32], '$k\\ge': [34], '2$': [35], 'integers,': [37], 'each': [38], 'them': [40], 'belonging': [41], 'specified': [44], 'interval.': [45], 'In': [46], 'particular,': [47], 'this': [48], 'gives': [49], 'estimate': [51], '$d_k(n)$.': [60]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3208033647', 'counts_by_year': [], 'updated_date': '2024-12-11T17:03:40.832684', 'created_date': '2021-11-08'}