Recent Preprints

  1. arxiv:2407.13788 New Borwein-type conjectures, Alexander Berkovich, Aritram Dhar. 6 pages.
  2. arxiv:2402.15886 Extension of Bressoud’s generalization of Borwein’s conjecture and some exact results, Alexander Berkovich, Aritram Dhar. 17 pages.
  3. arxiv:2312.15117 On partitions with bounded largest part and fixed integral GBG-rank modulo primes, Alexander Berkovich, Aritram Dhar. 16 pages.
  4. arxiv:2302.06017 On the q-binomial identities involving the Legendre symbol modulo 3, 8 pages.
  5. arXiv:2205.00527 On Finite Analogs of Schmidt’s Problem and Its Variants, Alexander Berkovich, Ali Kemal Uncu. 13 pages.
  6. arXiv:2111.13994 Bressoud’s identities for even moduli. New companions and related positivity result, Alexander Berkovich. 13 pages.
  7. arXiv:2106.09773 New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, Alexander Berkovich, Ali Kemal Uncu. 15 pages
  8. arXiv:2002.07986 Some New Positive Observations. Alexander Berkovich. 8 pages
  9. arXiv:1911.03707 Where do the maximum absolute q-series coefficients of (1−q)(1−q^2)(1−q^3)…(1−q^(n−1))(1−q^n) occur?, Alexander Berkovich, Ali Kemal Uncu. 9 pages
  10. arXiv:1810.12048 Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, Alexander Berkovich, Ali Kemal Uncu, 10 pages.
  11. arXiv:1810.06497 Elementary Polynomial Identities Involving q-Trinomial Coefficients, Alexander Berkovich, Ali Kemal Uncu. 9 pages.
  12. arXiv:1807.10974 Polynomial Identities Implying Capparelli’s Partition Theorems, Alexander Berkovich, Ali Kemal Uncu. 21 pages.
  13. arXiv:1708.01957 Some Elementary Partition Inequalities and Their Implications, Alexander Berkovich, Ali Kemal Uncu. 16 pages.
  14. arXiv:1705.07504 On some polynomials and series of Bloch-Polya Type, Alexander Berkovich, Ali Kemal Uncu. 9 pages.
  15. arXiv:1611.02217 Wronskians of theta functions and series for \(1/\pi\), Alexander Berkovich, Heng Huat Chan, Michael J. Schlosser. 35 pages.
  16. arXiv:1608.00193 New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions.  Alexander Berkovich, Ali Kemal Uncu. 17 pages.
  17. arXiv:1605.00291 Variation on a theme of Nathan Fine. New weighted partition identities. Alexander Berkovich, Ali Kemal Uncu. 16 pages.
  18. arXiv:1510.07301 On partitions with fixed number of even-indexed and odd-indexed odd parts.  Alexander Berkovich, Ali Kemal Uncu. 17 pages.
  19. arXiv:1504.02922 A New Companion to Capparelli’s Identities. Alexander Berkovich, Ali Kemal Uncu. 9 pages.
  20. arXiv:1406.7835 On The Gauss EYPHKA Theorem And Some Allied Inequalities. Alexander Berkovich. 12 pages.
  21. arXiv:1404.2693 Essentially Unique Representations by Certain Ternary Quadratic Forms. Alexander Berkovich, Frank Patane. 20 pages.
  22. arXiv:1306.5371 A partition inequality involving products of two \(q\)-Pochhammer symbols. Alexander Berkovich, Keith Grizzell. 14 pages.
  23. arXiv:1303.2362 On the class of dominant and subordinate products. Alexander Berkovich, Keith Grizzell. 10 pages.
  24. arXiv:1302.2359 Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients. Alexander Berkovich, Frank Patane. 23 pages.
  25. arXiv:1204.1092 On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients. Submitted to arXiv [math.NT]. Alexander Berkovich, Hamza Yesilyurt. 14 pages.
  26. arXiv:1112.3392 Races among products. Submitted to arXiv [math.NT]. Alexander Berkovich, Keith Grizzell. 9 pages.
  27. arXiv:1101.2951 On representation of an integer as the sum of three squares and the ternary quadratic forms with the discriminants \(p^2\), \(16p^2\). Alexander Berkovich, William Jagy. 17 pages.
  28. arXiv:1010.1926 A proof of the \(s\)-genus identities for ternary quadratic forms. Alexander Berkovich, Jonathan Hanke, William Jagy. 14 pages.
  29. arXiv:0907.1725 On Representation of an Integer by \(X^2 + Y^2 + Z^2\) and the Modular Equations of Degree 3 and 5. Alexander Berkovich. 16 pages.
  30. arXiv:0906.2848 Ternary Quadratic Forms, Modular Equations and Certain Positivity Conjectures. Alexander Berkovich, William Jagy. 24 pages.
  31. arXiv:0807.4727 The GBG-Rank and \(t\)-Cores I. Counting and 4-Cores. Alexander Berkovich, Frank G. Garvan. 15 pages.
  32. arXiv:0804.2038 On the representations of integers by the sextenary quadratic form \(x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2\) and 7-cores. Alexander Berkovich, Hamza Yesilyurt. 10 pages.
  33. An absolute value sum, American Mathematical Monthly 115, no. 3 (2008), p. 263. Matthias Beck, Alexander Berkovich.
  34. arXiv:0801.3008 The tri-pentagonal number theorem and related identities. Alexander Berkovich. 13 pages.
  35. arXiv:0712.4087 On the difference of partial theta functions. Alexander Berkovich. 6 pages.
  36. math.NT/0702027 K. Saito’s Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products. Alexander Berkovich, Frank G. Garvan. 15 pages.
  37. math.NT/0611300 Ramanujan’s Identities and Representation of Integers by Certain Binary and Quaternary Quadratic Forms. Alexander Berkovich, Hamza Yesilyurt. 26 pages.
  38. math.NT/0603150 New Identities for 7-cores with prescribed BG-rank. Alexander Berkovich, Hamza Yesilyurt. 12 pages.
  39. math.CO/0602362 The BG-rank of a partition and its applications. Alexander Berkovich, Frank G. Garvan. 20 pages.
  40. Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo 6, Probability and number theory—Kanazawa 2005, 21–39, Adv. Stud. Pure Math., 49, Math. Soc. Japan, Tokyo, 2007. Krishnaswami Alladi, Alexander Berkovich.
  41. math.CO/0409480 Dissecting the Stanley Partition Function. Alexander Berkovich, Frank G. Garvan. 11 pages.
  42. math.CO/0403167 Goellnitz-Gordon partitions with weights and parity conditions. Krishnaswami Alladi, Alexander Berkovich. 14 pages.
  43. math.CO/0402439 On the Andrews-Stanley Refinement of Ramanujan’s Partition Congruence Modulo 5 and Generalizations. Alexander Berkovich, Frank G. Garvan. 24 pages.
  44. math.CO/0302320 Positivity preserving transformations for \(q\)-binomial coefficients. Alexander Berkovich, S. Ole Warnaar. 58 pages.
  45. math.CO/0205055 A new four parameter q-series identity and its partition implications. Krishnaswami Alladi, George E. Andrews, Alexander Berkovich. 25 pages.
  46. math.CO/0205031 A limiting form of the \(q\)-Dixon \(_4\varphi {}_3\) summation and related partition identities. Krishnaswami Alladi, Alexander Berkovich. 12 pages.
  47. math.CO/0203111 Some Observations on Dyson’s New Symmetries of Partitions. Alexander Berkovich, Frank G. Garvan. 27 pages.
  48. math.CO/0203094 New polynomial analogues of Jacobi’s triple product and Lebesgue’s identities. Krishnaswami Alladi, Alexander Berkovich. 19 pages.
  49. math.CO/0109141 The WP-Bailey Tree and its Implications. George E. Andrews, Alexander Berkovich. 20 pages.