Journal
INTERNATIONAL JOURNAL OF NUMBER THEORY
Volume 17, Issue 3, Pages 787-804Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793042120400187
Keywords
Log-concavity; q-series; binomial coefficients; theta functions; elliptic functions; Turin's inequality
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Funding
- FWF Austrian Science Fund [F50-08, P32305, F50-10, F50-07, F50-09, F50-11]
- Austrian Science Fund (FWF) [P32305] Funding Source: Austrian Science Fund (FWF)
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In this study, discrete and continuous log-concavity results were established for a biparametric extension of the q-numbers and q-binomial coefficients. By utilizing classical results for the Jacobi theta function, some of the log-concavity results were extended to the elliptic setting. One of the main components of this analysis is a potentially new lemma involving a multiplicative analogue of Turkn's inequality.
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 Turkn's inequality.
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