A. Uncu

activity

20152025

most citedOn a weighted spin of the Lebesgue Identity

21 citations · 23 across the 7 of their papers we have counts for

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5 papers · 1 filter

math.NT2021

New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Alexander Berkovich, Ali Kemal Uncu

We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from…

math.NT2019★ 1 cited

Where do the maximum absolute $q$ -series coefficients of $(1 - q) (1 - q^{2}) (1 - q^{3}) \dots (1 - q^{n - 1}) (1 - q^{n})$ occur?

Alexander Berkovich, Ali K. Uncu

We used the MACH2 supercomputer to study coefficients in the $q$ -series expansion of $(1 - q) (1 - q^{2}) \dots (1 - q^{n})$ , for all $n \leq 75000$ . As a result, we were able to conjecture some…

math.NT2018

Elementary Polynomial Identities Involving $q$ -Trinomial Coefficients

Alexander Berkovich, Ali K. Uncu

We use $q$ -binomial theorem to prove three new polynomial identities involving $q$ -trinomial coefficients. We then use summation formulas for the $q$ -trinomial coefficients to conv…

math.NT2018

Refined $q$ -Trinomial Coefficients and Two Infinite Hierarchies of $q$ -Series Identities

Alexander Berkovich, Ali K. Uncu

We will prove an identity involving refined $q$ -trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transfor…

math.NT2018

Polynomial Identities Implying Capparelli's Partition Theorems

Alexander Berkovich, Ali K. Uncu

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews a…

New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Where do the maximum absolute q-series coefficients of (1−q)(1−q2)(1−q3)…(1−qn−1)(1−qn) occur?

Elementary Polynomial Identities Involving q-Trinomial Coefficients

Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities

Polynomial Identities Implying Capparelli's Partition Theorems

Where do the maximum absolute $q$ -series coefficients of $(1 - q) (1 - q^{2}) (1 - q^{3}) \dots (1 - q^{n - 1}) (1 - q^{n})$ occur?

Elementary Polynomial Identities Involving $q$ -Trinomial Coefficients

Refined $q$ -Trinomial Coefficients and Two Infinite Hierarchies of $q$ -Series Identities