2020/02/18 by Michael J. Schlosser, Schlosser, Michael J., Koushik Senapati +4
Mathematics · #05A20 (Primary) 05A10 #05A30 #11F27 #26D20 #33E05 (Secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CA #math.CO #msc:05A10 #msc:05A20 #msc:05A30 #msc:11F27 #msc:26D20 #msc:33E05
paper · pdf · doi:10.48550/arxiv.2002.07796
17 pages; dedicated to Bruce Berndt, on the occasion of his 80th birthday; minor changes; to appear in the International Journal of Number Theory
openalex publication_date 2020/02/18 · arxiv created 2020/08/11 · arxiv updated 2020/08/12 · openalex created_date 2022/07/18 · openalex updated_date 2026/07/28
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 Turán's inequality.