On a conjecture of Kaneko and Ohno

Name: Work Video:
Duration: 3 min 30 s
Description: Let X 0 (k, n, s) denote the sum of all multiple zeta-star values of weight k, depth n and height s.Kaneko and Ohno conjectured that, for any positive integers m, n, s with m, n ≥ s, the differencecan be expressed as a polynomial of zeta values with rational coefficients.
Zhonghua Li
{'id': 'https://openalex.org/W1970595609', 'doi': 'https://doi.org/10.2140/pjm.2012.257.419', 'title': 'On a conjecture of Kaneko and Ohno', 'display_name': 'On a conjecture of Kaneko and Ohno', 'publication_year': 2012, 'publication_date': '2012-07-04', 'ids': {'openalex': 'https://openalex.org/W1970595609', 'doi': 'https://doi.org/10.2140/pjm.2012.257.419', 'mag': '1970595609'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/pjm.2012.257.419', 'pdf_url': 'http://msp.org/pjm/2012/257-2/pjm-v257-n2-p07-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], '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': 'http://msp.org/pjm/2012/257-2/pjm-v257-n2-p07-s.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5100398093', 'display_name': 'Zhonghua Li', 'orcid': 'https://orcid.org/0000-0002-0927-226X'}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Zhong-hua Li', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5100398093'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 2.075, 'has_fulltext': False, 'cited_by_count': 12, 'citation_normalized_percentile': {'value': 0.808245, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 86, 'max': 87}, 'biblio': {'volume': '257', 'issue': '2', 'first_page': '419', 'last_page': '430'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11428', 'display_name': 'Advanced Mathematical Identities', '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/T11428', 'display_name': 'Advanced Mathematical Identities', '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/T11166', 'display_name': 'Analytic Number Theory Research', 'score': 0.9979, '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/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 0.9606, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/star', 'display_name': 'Star (game theory)', 'score': 0.7595859}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.93649864}, {'id': 'https://openalex.org/C2780990831', 'wikidata': 'https://www.wikidata.org/wiki/Q319141', 'display_name': 'Conjecture', 'level': 2, 'score': 0.8204329}, {'id': 'https://openalex.org/C2780897414', 'wikidata': 'https://www.wikidata.org/wiki/Q7600592', 'display_name': 'Star (game theory)', 'level': 2, 'score': 0.7595859}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.5739907}, {'id': 'https://openalex.org/C90119067', 'wikidata': 'https://www.wikidata.org/wiki/Q43260', 'display_name': 'Polynomial', 'level': 2, 'score': 0.47920188}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.32779944}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.1774222}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/pjm.2012.257.419', 'pdf_url': 'http://msp.org/pjm/2012/257-2/pjm-v257-n2-p07-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1106.5103', 'pdf_url': 'https://arxiv.org/pdf/1106.5103', '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/10.2140/pjm.2012.257.419', 'pdf_url': 'http://msp.org/pjm/2012/257-2/pjm-v257-n2-p07-s.pdf', 'source': {'id': 'https://openalex.org/S130774151', 'display_name': 'Pacific Journal of Mathematics', 'issn_l': '0030-8730', 'issn': ['0030-8730', '1945-5844'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 8, 'referenced_works': ['https://openalex.org/W1970525340', 'https://openalex.org/W1983199293', 'https://openalex.org/W1999993616', 'https://openalex.org/W2000117364', 'https://openalex.org/W2007561349', 'https://openalex.org/W2044903464', 'https://openalex.org/W2091205496', 'https://openalex.org/W2103840417'], 'related_works': ['https://openalex.org/W4375956809', 'https://openalex.org/W4297950433', 'https://openalex.org/W4292635168', 'https://openalex.org/W4288279572', 'https://openalex.org/W4287023968', 'https://openalex.org/W4286909116', 'https://openalex.org/W3194471551', 'https://openalex.org/W2784911598', 'https://openalex.org/W1973978937', 'https://openalex.org/W1581373162'], 'abstract_inverted_index': {'Let': [0], 'X': [1], '0': [2], '(k,': [3], 'n,': [4, 31], 's)': [5], 'denote': [6], 'the': [7, 38], 'sum': [8], 'of': [9, 14, 45], 'all': [10], 'multiple': [11], 'zeta-star': [12], 'values': [13, 47], 'weight': [15], 'k,': [16], 'depth': [17], 'n': [18, 35], 'and': [19, 22], 'height': [20], 's.Kaneko': [21], 'Ohno': [23], 'conjectured': [24], 'that,': [25], 'for': [26], 'any': [27], 'positive': [28], 'integers': [29], 'm,': [30, 34], 's': [32], 'with': [33, 48], '≥': [36], 's,': [37], 'differencecan': [39], 'be': [40], 'expressed': [41], 'as': [42], 'a': [43], 'polynomial': [44], 'zeta': [46], 'rational': [49], 'coefficients.': [50]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1970595609', 'counts_by_year': [{'year': 2023, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 2}, {'year': 2016, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 3}, {'year': 2012, 'cited_by_count': 2}], 'updated_date': '2024-12-15T17:29:21.252682', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
