从杰克逊的ϕ78求和与沃森的ϕ78变换中得出的q-超级共轭关系

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2024-01-12 DOI:10.1016/j.jcta.2023.105853

Chuanan Wei

{"title":"从杰克逊的ϕ78求和与沃森的ϕ78变换中得出的q-超级共轭关系","authors":"Chuanan Wei","doi":"10.1016/j.jcta.2023.105853","DOIUrl":null,"url":null,"abstract":"<div>q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's <math><mmultiscripts><mrow><mi>ϕ</mi></mrow><mrow><mn>7</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>8</mn></mrow><none></none></mmultiscripts></math> summation, Watson's <math><mmultiscripts><mrow><mi>ϕ</mi></mrow><mrow><mn>7</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>8</mn></mrow><none></none></mmultiscripts></math> transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773–808] and two q-supercongruences involving double series.</div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation\",\"authors\":\"Chuanan Wei\",\"doi\":\"10.1016/j.jcta.2023.105853\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's <math><mmultiscripts><mrow><mi>ϕ</mi></mrow><mrow><mn>7</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>8</mn></mrow><none></none></mmultiscripts></math> summation, Watson's <math><mmultiscripts><mrow><mi>ϕ</mi></mrow><mrow><mn>7</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>8</mn></mrow><none></none></mmultiscripts></math> transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773–808] and two q-supercongruences involving double series.</div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316523001218\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316523001218","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

环状多项式的五次幂和六次幂的 q 上共轭在文献中非常罕见。在本文中，我们根据杰克逊的ϕ78求和、沃森的ϕ78变换、郭和祖迪林最近提出的创造性微分法以及中国余数定理，建立了一些环状多项式的五次和六次幂的 q 次共轭。更具体地说，我们给出了 Long 和 Ramakrishna [Adv. Math. 290 (2016), 773-808] 提出的一个漂亮公式的 q-analogue 以及两个涉及双数列的 q-supercongruences 。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

q-Supercongruences from Jackson's ϕ78 summation and Watson's ϕ78 transformation

q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's ${}_{8}ϕ_{7}$ summation, Watson's ${}_{8}ϕ_{7}$ transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773–808] and two q-supercongruences involving double series.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.