About

Alexander Berkovich is a Professor of Mathematics at the University of Florida. He was awarded the University of Florida Term Professorship from 2017 to 2020, recognizing his contributions to the academic community. His research interests lie primarily in additive number theory, with a focus on partitions, combinatorics, and basic q-hypergeometric series. Additionally, he works in the field of mathematical physics, particularly on quantum exactly integrable models, conformal field theory, and special functions. Professor Berkovich is actively involved in teaching, offering courses such as Introductory Number Theory and Abstract Algebra. He maintains regular office hours at the University of Florida's Department of Mathematics, where he is based in Little Hall.

Research topics

• Pure mathematics
• Mathematics
• Combinatorics
• Geology
• Applied mathematics

Selected publications

• Further applications of cubic q-binomial transformations

  Discrete Mathematics · 2026-05-07

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• New Borwein-Type Conjectures

  Experimental Mathematics · 2025-03-07

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• Finite analogs of partition bias related to hook length two and a variant of Sylvester’s map

  The Ramanujan Journal · 2025-07-18 · 1 citations

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• Extension of Bressoud’s generalization of Borwein’s conjecture and some exact results

  The Ramanujan Journal · 2025-03-21

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• New Borwein-type conjectures

  arXiv (Cornell University) · 2024-07-13

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  Motivated by recent research of Wang and Krattenthaler, we use Maple to propose five new ``Borwein-type'' conjectures modulo $3$ and two new ``Borwein-type'' conjectures modulo $5$.

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• On Partitions with Bounded Largest Part and Fixed Integral GBG-rank Modulo Primes

  Annals of Combinatorics · 2024-12-09 · 2 citations

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• Extension of Bressoud's generalization of Borwein's conjecture and some exact results

  arXiv (Cornell University) · 2024-02-24

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  In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the infinite families.

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• On the q-binomial identities involving the Legendre symbol modulo 3

  arXiv (Cornell University) · 2023-02-12

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  I use polynomial analogue of the Jacobi triple product identity together with the Eisenstein formula for the Legendre symbol modulo 3 . to prove six identities involving the $q$-binomial coefficients. These identities are then extended to the new infinite hierarchies of q-series identities by means of the special case of Bailey's lemma. Some of the identities of Ramanujan, Slater, McLaughlin and Sills are obtained this way.

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• On partitions with bounded largest part and fixed integral GBG-rank modulo primes

  arXiv (Cornell University) · 2023-12-22

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  In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo $t$ which is a generalization of the well-known BG-rank. In this paper, we use the Littlewood decomposition of partitions to study partitions with bounded largest part and fixed integral value of GBG-rank modulo primes. As a consequence, we obtain new elegant generating function formulas for unrestricted partitions, self-conjugate partitions, and partitions whose parts repeat a finite number of times.

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• On the q-binomial identities involving the Legendre symbol modulo 3

  Discrete Mathematics · 2023-12-01 · 1 citations

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Frequent coauthors

• Ali Kemal Uncu

  42 shared

• Barry M. McCoy

  The University of Tokyo

  24 shared

• Krishnaswami Alladi

  22 shared

• Ganpathy Murthy

  16 shared

• Frank G. Garvan

  15 shared

• Hamza Yesilyurt

  Bilkent University

  10 shared

• George E. Andrews

  8 shared

• Frank Patane

  Samford University

  7 shared

Awards & honors

• University of Florida Term Professorship (2017-2020)