{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:08:31Z","timestamp":1757617711301,"version":"3.44.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s10998-025-00637-1","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T17:31:47Z","timestamp":1744133507000},"page":"1-9","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A generalization of a Menon-type identity by T\u00f3th in residually finite Dedekind domains"],"prefix":"10.1007","volume":"91","author":[{"given":"Tianfang","family":"Qi","sequence":"first","affiliation":[]},{"given":"Man","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"key":"637_CR1","unstructured":"M. Chen, S. Hu, Y. Li, On Menon\u2013Sury\u2019s identity with several Dirichlet characters, arXiv:1807.07241"},{"key":"637_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5486\/PMD.2021.8731","volume":"98","author":"M Chen","year":"2021","unstructured":"M. Chen, T. Qi, A Menon-Sury-type identity for arithmetic functions on $${\\mathbb{F} }_{q}[T]$$. Publ. Math. Debrecen 98, 1\u201314 (2021)","journal-title":"Publ. Math. Debrecen"},{"key":"637_CR3","doi-asserted-by":"crossref","unstructured":"M. Chen, Z. Zheng, A Menon-type identity with Dirichlet characters in residually finite Dedekind domains Ramanujan J. 57, 1473\u20131488 (2022)","DOI":"10.1007\/s11139-021-00448-1"},{"issue":"3","key":"637_CR4","first-page":"331","volume":"53","author":"P Haukkanen","year":"1996","unstructured":"P. Haukkanen, J. Wang, A generalization of Menon\u2019s identity with respect to a set of polynomials. Portugal. Math. 53(3), 331\u2013337 (1996)","journal-title":"Portugal. Math."},{"issue":"1","key":"637_CR5","first-page":"37","volume":"39","author":"P Haukkanen","year":"1997","unstructured":"P. Haukkanen, J. Wang, High degree analogs of Menon\u2019s identity. Indian J. Math. 39(1), 37\u201342 (1997)","journal-title":"Indian J. Math."},{"key":"637_CR6","doi-asserted-by":"publisher","first-page":"2631","DOI":"10.1142\/S1793042118501579","volume":"14","author":"Y Li","year":"2018","unstructured":"Y. Li, X. Hu, D. Kim, A generalization of Menon\u2019s identity with Dirichlet characters. Int. J. Number Theory. 14, 2631\u20132639 (2018)","journal-title":"Int. J. Number Theory."},{"issue":"3","key":"637_CR7","doi-asserted-by":"publisher","first-page":"545","DOI":"10.11650\/tjm\/180702","volume":"23","author":"Y Li","year":"2019","unstructured":"Y. Li, X. Hu, D. Kim, A Menon-type identity with multiplicative and additive characters. Taiwanese J. Math. 23(3), 545\u2013555 (2019)","journal-title":"Taiwanese J. Math."},{"key":"637_CR8","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.jnt.2016.11.023","volume":"175","author":"Y Li","year":"2017","unstructured":"Y. Li, D. Kim, A Menon-type identity with many tuples of group of units in residually finite Dedekind domains. J. Number Theory. 175, 42\u201350 (2017)","journal-title":"J. Number Theory."},{"key":"637_CR9","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.jnt.2017.03.016","volume":"179","author":"Y Li","year":"2017","unstructured":"Y. Li, D. Kim, Menon-type identities derived from actions of subgroups of general linear groups. J. Number Theory. 179, 97\u2013112 (2017)","journal-title":"J. Number Theory."},{"key":"637_CR10","first-page":"155","volume":"29","author":"PK Menon","year":"1965","unstructured":"P.K. Menon, On the sum $$\\sum (a-1, n)[(a, n)=1]$$. J. Indian Math. Soc. (N.S.) 29, 155\u2013163 (1965)","journal-title":"J. Indian Math. Soc. (N.S.)"},{"key":"637_CR11","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.jnt.2013.11.003","volume":"137","author":"C Miguel","year":"2014","unstructured":"C. Miguel, Menon\u2019s identity in residually finite Dedekind domains. J. Number Theory. 137, 179\u2013185 (2014)","journal-title":"J. Number Theory."},{"key":"637_CR12","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.jnt.2015.12.018","volume":"164","author":"C Miguel","year":"2016","unstructured":"C. Miguel, A Menon-type identity in residually finite Dedekind domains. J. Number Theory. 164, 43\u201351 (2016)","journal-title":"J. Number Theory."},{"key":"637_CR13","unstructured":"E.A. Molla, S. Sarkar, A generalization of T\u00f3th identity in $${\\mathbb{F}}_{q}[T]$$ involving a Dirichlet character, (2022), arXiv: 2206.03184v1"},{"key":"637_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07001-7","volume-title":"Elementary and Analytic Theory of Algebraic Numbers","author":"W Narkiewicz","year":"2004","unstructured":"W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers (Springer-Vorlag, Berlin, 2004)"},{"key":"637_CR15","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s12215-009-0010-6","volume":"58","author":"B Sury","year":"2009","unstructured":"B. Sury, Some number-theoretic identities from group actions. Rend. Circ. Mat. Palermo. 58, 99\u2013108 (2009)","journal-title":"Rend. Circ. Mat. Palermo."},{"key":"637_CR16","first-page":"97","volume":"69","author":"L T\u00f3th","year":"2011","unstructured":"L. T\u00f3th, Menon\u2019s identity and arithmetical sums representing functions of several variables. Rend. Semin. Mat. Univ. Politec. Torino. 69, 97\u2013110 (2011)","journal-title":"Rend. Semin. Mat. Univ. Politec. Torino."},{"key":"637_CR17","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1142\/S179304211850063X","volume":"14","author":"L T\u00f3th","year":"2018","unstructured":"L. T\u00f3th, Menon-type identities concerning Dirichlet characters. Int. J. Number Theory. 14, 1047\u20131054 (2018)","journal-title":"Int. J. Number Theory."},{"issue":"3","key":"637_CR18","doi-asserted-by":"publisher","first-page":"557","DOI":"10.11650\/tjm\/180904","volume":"23","author":"L T\u00f3th","year":"2019","unstructured":"L. T\u00f3th, Short proof and generalization of a Menon-type identity by Li, Hu and Kim. Taiwanese J. Math. 23(3), 557\u2013561 (2019)","journal-title":"Taiwanese J. Math."},{"issue":"1","key":"637_CR19","doi-asserted-by":"publisher","first-page":"142","DOI":"10.2478\/ausm-2023-0009","volume":"15","author":"L T\u00f3th","year":"2023","unstructured":"L. T\u00f3th, Proofs, generalizations and analogs of Menon\u2019s identity: a survey, Acta Univ. Sapientiae, Mathematica. 15(1), 142\u2013197 (2023)","journal-title":"Sapientiae, Mathematica."},{"issue":"9","key":"637_CR20","doi-asserted-by":"publisher","first-page":"2373","DOI":"10.1142\/S1793042117501299","volume":"13","author":"X Zhao","year":"2017","unstructured":"X. Zhao, Z. Cao, Another generalization of Menon\u2019s identity. Int. J. Number Theory. 13(9), 2373\u20132379 (2017)","journal-title":"Int. J. Number Theory."},{"key":"637_CR21","first-page":"213","volume":"160","author":"Z Zheng","year":"2020","unstructured":"Z. Zheng, M. Chen, Z. Hong, On Ramanujan sums over a Dedekind Domain with finite norm property, accepted. Acta Math Sin, Engl Ser. 160, 213\u2013221 (2020)","journal-title":"Acta Math Sin, Engl Ser."},{"issue":"5","key":"637_CR22","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1142\/S1793042122500543","volume":"18","author":"Z Zheng","year":"2022","unstructured":"Z. Zheng, M. Chen, J. Xu, On Gauss Sums over Dedekind Domains. Int. J. Number Theory. 18(5), 1047\u20131063 (2022)","journal-title":"Int. J. Number Theory."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00637-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-025-00637-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-025-00637-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T10:43:26Z","timestamp":1757155406000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-025-00637-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,8]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["637"],"URL":"https:\/\/doi.org\/10.1007\/s10998-025-00637-1","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"type":"print","value":"0031-5303"},{"type":"electronic","value":"1588-2829"}],"subject":[],"published":{"date-parts":[[2025,4,8]]},"assertion":[{"value":"4 February 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}