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Some $q$-congruences with the Carlitz formulas
대한수학회 (The Korean Mathematical Society)|2025.11|대한수학회지 (Journal of the KMS)|제62권 제6호|pp. 1509-1523|DOI 10.4134/JKMS.j240486
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This article applies an equivalent form of the Carlitz formula, as introduced by the third author, to derive two new $q$-congruences modulo the square of a cyclotomic polynomial and provides detailed examples of these $q$-congruences. These developments substantially advance the research previously conducted by Guo et al.
Abstract
This article applies an equivalent form of the Carlitz formula, as introduced by the third author, to derive two new $q$-congruences modulo the square of a cyclotomic polynomial and provides detailed examples of these $q$-congruences. These developments substantially advance the research previously conducted by Guo et al.
관련 논문AI추천
A NEW q-ANALOGUE OF VAN HAMME’S (G.2) SUPERCONGRUENCE FOR PRIMES p ≡ 3 (mod 4)Victor J. W. Guo, Xiuguo Lian대한수학회 · 대한수학회보2023 · 제60권 제3호A note on Carlitz's type q-Changhee numbers and polynomials권혁인, 김태균, 장관우, Dmitry V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제4호On congruences involving the generalized Catalan numbers and harmonic numbersNese Omur, Sibel Koparal대한수학회 · 대한수학회보2019 · 제56권 제3호Expansions of generalized Carlitz -Bernoulli polynomials김대산, 김태균, 서종진, 이상훈장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제2호A note on the modified q-Bernoulli polynomials권종겸, 박진우, 서종진, 임석훈장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제4호New congruences with the generalized Catalan numbers and harmonic numbersLaid Elkhiri, Nese Omur, Sibel Koparal대한수학회 · 대한수학회보2021 · 제58권 제5호
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