{"title":"双参数和q-二项式系数的椭圆扩展的对数凹性结果","authors":"M. Schlosser, K. Senapati, A. Uncu","doi":"10.1142/s1793042120400187","DOIUrl":null,"url":null,"abstract":"We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our log-concavity results to the elliptic setting. One of our main ingredients is a putatively new lemma involving a multiplicative analogue of Turan's inequality.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"475 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients\",\"authors\":\"M. Schlosser, K. Senapati, A. Uncu\",\"doi\":\"10.1142/s1793042120400187\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our log-concavity results to the elliptic setting. One of our main ingredients is a putatively new lemma involving a multiplicative analogue of Turan's inequality.\",\"PeriodicalId\":8451,\"journal\":{\"name\":\"arXiv: Classical Analysis and ODEs\",\"volume\":\"475 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793042120400187\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793042120400187","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients
We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our log-concavity results to the elliptic setting. One of our main ingredients is a putatively new lemma involving a multiplicative analogue of Turan's inequality.
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