Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2963392070', 'doi': 'https://doi.org/10.1112/s1461157010000215', 'title': 'On the zeros of Dirichlet -functions', 'display_name': 'On the zeros of Dirichlet -functions', 'publication_year': 2011, 'publication_date': '2011-01-01', 'ids': {'openalex': 'https://openalex.org/W2963392070', 'doi': 'https://doi.org/10.1112/s1461157010000215', 'mag': '2963392070'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1112/s1461157010000215', 'pdf_url': 'https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CF36DD3B48E5378D26C5EBB93FEA9A61/S1461157010000215a.pdf/div-class-title-on-the-zeros-of-dirichlet-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20180507065314215-0750-s1461157010000215-s1461157010000215-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-l-span-span-span-span-functions-div.pdf', 'source': {'id': 'https://openalex.org/S118668765', 'display_name': 'LMS Journal of Computation and Mathematics', 'issn_l': '1461-1570', 'issn': ['1461-1570'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311874', 'host_organization_name': 'London Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310311874'], 'host_organization_lineage_names': ['London Mathematical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CF36DD3B48E5378D26C5EBB93FEA9A61/S1461157010000215a.pdf/div-class-title-on-the-zeros-of-dirichlet-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20180507065314215-0750-s1461157010000215-s1461157010000215-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-l-span-span-span-span-functions-div.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5085908966', 'display_name': 'Sami Omar', 'orcid': 'https://orcid.org/0000-0002-3028-7618'}, 'institutions': [{'id': 'https://openalex.org/I82952536', 'display_name': 'King Khalid University', 'ror': 'https://ror.org/052kwzs30', 'country_code': 'SA', 'type': 'education', 'lineage': ['https://openalex.org/I82952536']}], 'countries': ['SA'], 'is_corresponding': False, 'raw_author_name': 'Sami Omar', 'raw_affiliation_strings': ['Department of Mathematics, King Khalid University, Abha 9004, Saudi Arabia'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, King Khalid University, Abha 9004, Saudi Arabia', 'institution_ids': ['https://openalex.org/I82952536']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5076078257', 'display_name': 'Raouf Ouni', 'orcid': 'https://orcid.org/0000-0002-9382-6949'}, 'institutions': [{'id': 'https://openalex.org/I82952536', 'display_name': 'King Khalid University', 'ror': 'https://ror.org/052kwzs30', 'country_code': 'SA', 'type': 'education', 'lineage': ['https://openalex.org/I82952536']}], 'countries': ['SA'], 'is_corresponding': False, 'raw_author_name': 'Raouf Ouni', 'raw_affiliation_strings': ['Department of Mathematics Faculty of Science of Tunis 2092 Tunis Tunisia', 'Department of Mathematics King Khalid University Abha 9004 Saudi Arabia'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics Faculty of Science of Tunis 2092 Tunis Tunisia', 'institution_ids': []}, {'raw_affiliation_string': 'Department of Mathematics King Khalid University Abha 9004 Saudi Arabia', 'institution_ids': ['https://openalex.org/I82952536']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5064599832', 'display_name': 'Kamel Mazhouda', 'orcid': 'https://orcid.org/0000-0002-7284-9404'}, 'institutions': [{'id': 'https://openalex.org/I166928557', 'display_name': 'University of Monastir', 'ror': 'https://ror.org/00nhtcg76', 'country_code': 'TN', 'type': 'education', 'lineage': ['https://openalex.org/I166928557']}, {'id': 'https://openalex.org/I82952536', 'display_name': 'King Khalid University', 'ror': 'https://ror.org/052kwzs30', 'country_code': 'SA', 'type': 'education', 'lineage': ['https://openalex.org/I82952536']}], 'countries': ['SA', 'TN'], 'is_corresponding': False, 'raw_author_name': 'Kamel Mazhouda', 'raw_affiliation_strings': ['Department of Mathematics Faculty of Science of Monastir 5000 Monastir Tunisia', 'Department of Mathematics King Khalid University Abha 9004 Saudi Arabia'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics Faculty of Science of Monastir 5000 Monastir Tunisia', 'institution_ids': ['https://openalex.org/I166928557']}, {'raw_affiliation_string': 'Department of Mathematics King Khalid University Abha 9004 Saudi Arabia', 'institution_ids': ['https://openalex.org/I82952536']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 6.883, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 49, 'citation_normalized_percentile': {'value': 0.899506, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 95, 'max': 96}, 'biblio': {'volume': '14', 'issue': None, 'first_page': '140', 'last_page': '154'}, 'is_retracted': True, 'is_paratext': 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': 0.9983, '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/T12504', 'display_name': 'Mathematics and Applications', 'score': 0.9977, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, '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/analytic-number-theory', 'display_name': 'Analytic number theory', 'score': 0.7883315}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8507068}, {'id': 'https://openalex.org/C149381693', 'wikidata': 'https://www.wikidata.org/wiki/Q10843274', 'display_name': 'Analytic number theory', 'level': 2, 'score': 0.7883315}, {'id': 'https://openalex.org/C199479865', 'wikidata': 'https://www.wikidata.org/wiki/Q205966', 'display_name': 'Riemann hypothesis', 'level': 2, 'score': 0.61831754}, {'id': 'https://openalex.org/C207803063', 'wikidata': 'https://www.wikidata.org/wiki/Q620595', 'display_name': 'Dirichlet series', 'level': 4, 'score': 0.57249683}, {'id': 'https://openalex.org/C169214877', 'wikidata': 'https://www.wikidata.org/wiki/Q981016', 'display_name': 'Dirichlet distribution', 'level': 3, 'score': 0.56566644}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.47474056}, {'id': 'https://openalex.org/C2777686260', 'wikidata': 'https://www.wikidata.org/wiki/Q144037', 'display_name': 'Calculus (dental)', 'level': 2, 'score': 0.3348481}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.28638652}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.27615112}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.16355696}, {'id': 'https://openalex.org/C71924100', 'wikidata': 'https://www.wikidata.org/wiki/Q11190', 'display_name': 'Medicine', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C199343813', 'wikidata': 'https://www.wikidata.org/wiki/Q12128', 'display_name': 'Dentistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C182310444', 'wikidata': 'https://www.wikidata.org/wiki/Q1332643', 'display_name': 'Boundary value problem', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1112/s1461157010000215', 'pdf_url': 'https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CF36DD3B48E5378D26C5EBB93FEA9A61/S1461157010000215a.pdf/div-class-title-on-the-zeros-of-dirichlet-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20180507065314215-0750-s1461157010000215-s1461157010000215-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-l-span-span-span-span-functions-div.pdf', 'source': {'id': 'https://openalex.org/S118668765', 'display_name': 'LMS Journal of Computation and Mathematics', 'issn_l': '1461-1570', 'issn': ['1461-1570'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311874', 'host_organization_name': 'London Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310311874'], 'host_organization_lineage_names': ['London Mathematical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1507.03431', 'pdf_url': 'http://arxiv.org/pdf/1507.03431', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1112/s1461157010000215', 'pdf_url': 'https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CF36DD3B48E5378D26C5EBB93FEA9A61/S1461157010000215a.pdf/div-class-title-on-the-zeros-of-dirichlet-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-gif-data-type-simple-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20180507065314215-0750-s1461157010000215-s1461157010000215-inline1-gif-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-l-span-span-span-span-functions-div.pdf', 'source': {'id': 'https://openalex.org/S118668765', 'display_name': 'LMS Journal of Computation and Mathematics', 'issn_l': '1461-1570', 'issn': ['1461-1570'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311874', 'host_organization_name': 'London Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310311874'], 'host_organization_lineage_names': ['London Mathematical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 13, 'referenced_works': ['https://openalex.org/W1498769399', 'https://openalex.org/W1502461188', 'https://openalex.org/W1971436563', 'https://openalex.org/W2013554324', 'https://openalex.org/W2029579397', 'https://openalex.org/W2039040097', 'https://openalex.org/W2045840473', 'https://openalex.org/W2072317848', 'https://openalex.org/W2090793615', 'https://openalex.org/W218433857', 'https://openalex.org/W2313883396', 'https://openalex.org/W2963392070', 'https://openalex.org/W3099520404'], 'related_works': ['https://openalex.org/W4286908302', 'https://openalex.org/W4255421128', 'https://openalex.org/W4246602673', 'https://openalex.org/W2981923301', 'https://openalex.org/W2904221364', 'https://openalex.org/W2390429293', 'https://openalex.org/W2182380262', 'https://openalex.org/W2050208332', 'https://openalex.org/W2012867998', 'https://openalex.org/W1514073005'], 'abstract_inverted_index': {'This': [0], 'paper': [1], '[1],': [2], 'which': [3], 'was': [4, 34], 'published': [5], 'online': [6], 'on': [7], '1': [8], 'June': [9], '2011,': [10], 'has': [11], 'been': [12], 'retracted': [13], 'by': [14], 'agreement': [15], 'between': [16], 'the': [17, 19, 24, 52, 55, 59, 94, 110], 'authors,': [18], 'journal’s': [20], 'Editor-in-Chief': [21], 'Derek': [22], 'Holt,': [23], 'London': [25], 'Mathematical': [26], 'Society': [27], 'and': [28, 50, 70, 98], 'Cambridge': [29], 'University': [30], 'Press.': [31], 'The': [32], 'retraction': [33], 'agreed': [35], 'to': [36], 'prevent': [37], 'other': [38], 'authors': [39], 'from': [40], 'using': [41, 63, 106], 'incorrect': [42], 'mathematical': [43], 'results.': [44], '(In': [45], 'this': [46], 'paper,': [47], 'we': [48, 89, 99], 'compute': [49], 'verify': [51], 'positivity': [53], 'of': [54], 'Li': [56, 111], 'coefficients': [57], 'for': [58, 93, 104, 109], 'Dirichlet': [60], '$L$': [61], '-functions': [62], 'an': [64], 'arithmetic': [65], 'formula': [66], 'established': [67], 'in': [68], 'Omar': [69], 'Mazhouda,': [71], 'J.': [72, 80], 'Number': [73, 81], 'Theory': [74, 82], '125': [75], '(2007)': [76], 'no.': [77, 85], '1,': [78], '50–58;': [79], '130': [83], '(2010)': [84], '4,': [86], '1109–1114.': [87], 'Furthermore,': [88], 'formulate': [90], 'a': [91], 'criterion': [92], 'partial': [95], 'Riemann': [96], 'hypothesis': [97], 'provide': [100], 'some': [101], 'numerical': [102], 'evidence': [103], 'it': [105], 'new': [107], 'formulas': [108], 'coefficients.)': [112]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2963392070', 'counts_by_year': [{'year': 2021, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 4}, {'year': 2018, 'cited_by_count': 3}, {'year': 2017, 'cited_by_count': 8}, {'year': 2016, 'cited_by_count': 5}, {'year': 2015, 'cited_by_count': 7}, {'year': 2014, 'cited_by_count': 6}, {'year': 2013, 'cited_by_count': 5}, {'year': 2012, 'cited_by_count': 4}], 'updated_date': '2024-12-14T20:45:02.218975', 'created_date': '2019-07-30'}