{"id":188,"date":"2013-12-15T10:20:35","date_gmt":"2013-12-15T15:20:35","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/alexb\/?page_id=188"},"modified":"2026-03-19T08:12:42","modified_gmt":"2026-03-19T12:12:42","slug":"recent-preprints","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/alexb\/recent-preprints\/","title":{"rendered":"Recent Preprints"},"content":{"rendered":"\r\n
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Recent Preprints<\/h1>\n\n\n\n
  1. arxiv:2510.00130<\/a> Further applications of cubic q-binomial transformations, Alexander Berkovich, Aritram Dhar. 11 pages.<\/li>\n
  2. arxiv:2503.17571<\/a> Finite analogs of partition bias related to hook length two and a variant of Sylvester’s map, Alexander Berkovich, Aritram Dhar. 20 pages.<\/li>\n
  3. arxiv:2407.13788<\/a> New Borwein-type conjectures, Alexander Berkovich, Aritram Dhar. 7 pages.<\/li>\n
  4. arxiv:2402.15886<\/a> Extension of Bressoud’s generalization of Borwein’s conjecture and some exact results, Alexander Berkovich, Aritram Dhar. 17 pages.<\/li>\n
  5. arxiv:2312.15117<\/a> On partitions with bounded largest part and fixed integral GBG-rank modulo primes, Alexander Berkovich, Aritram Dhar. 17 pages.<\/li>\n
  6. arxiv:2302.06017<\/a> On the q-binomial identities involving the Legendre symbol modulo 3, 8 pages.<\/li>\n
  7. arXiv:2205.00527<\/a> On Finite Analogs of Schmidt’s Problem and Its Variants, Alexander Berkovich, Ali Kemal Uncu. 13 pages.<\/li>\n
  8. arXiv:2111.13994<\/a> Bressoud’s identities for even moduli. New companions and related positivity result, Alexander Berkovich. 13 pages.<\/li>\n
  9. arXiv:2106.09773<\/a> New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, Alexander Berkovich, Ali Kemal Uncu. 15 pages<\/li>\n
  10. arXiv:2002.07986<\/a> Some New Positive Observations. Alexander Berkovich. 8 pages<\/li>\n
  11. arXiv:1911.03707<\/a> Where do the maximum absolute q<\/span><\/span><\/span><\/span>-series coefficients of (<\/span>1<\/span>\u2212<\/span>q<\/span>)<\/span>(<\/span>1<\/span>\u2212<\/span>q^<\/span>2<\/span><\/span>)<\/span>(<\/span>1<\/span>\u2212<\/span>q^<\/span>3<\/span><\/span>)<\/span>\u2026<\/span>(<\/span>1<\/span>\u2212<\/span>q^(<\/span>n<\/span>\u2212<\/span>1)<\/span><\/span><\/span><\/span>)<\/span>(<\/span>1<\/span>\u2212<\/span>q^<\/span>n<\/span><\/span>)<\/span><\/span><\/span><\/span> occur?, Alexander Berkovich, Ali Kemal Uncu. 9 pages<\/li>\n
  12. arXiv:1810.12048<\/a>\u00a0Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series\u00a0Identities,\u00a0Alexander Berkovich, Ali Kemal Uncu, 10 pages.<\/span><\/li>\n
  13. arXiv:1810.06497<\/a> Elementary Polynomial Identities Involving\u00a0q<\/span><\/span><\/span><\/span>-Trinomial Coefficients,<\/span>\u00a0Alexander Berkovich, Ali Kemal Uncu. 9 pages.<\/span><\/li>\n
  14. arXiv:1807.10974<\/a> Polynomial Identities Implying Capparelli’s Partition Theorems,\u00a0Alexander Berkovich, Ali Kemal Uncu. 21 pages.<\/li>\n
  15. arXiv:1708.01957<\/a>\u00a0Some Elementary Partition Inequalities and Their Implications,\u00a0Alexander Berkovich, Ali Kemal Uncu. 16 pages.<\/li>\n
  16. arXiv:1705.07504<\/a>\u00a0On some polynomials and series of Bloch-Polya Type, Alexander Berkovich, Ali Kemal Uncu. 9 pages.<\/li>\n
  17. arXiv:1611.02217<\/a> Wronskians of theta functions and series for \\(1\/pi\\),\u00a0Alexander Berkovich, Heng Huat Chan, Michael J. Schlosser. 35 pages.<\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
  18. arXiv:1608.00193<\/a>\u00a0New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions.\u00a0\u00a0Alexander Berkovich, Ali Kemal Uncu. 17 pages.<\/li>\n
  19. arXiv:1605.00291<\/a>\u00a0Variation on a theme of Nathan Fine. New weighted partition identities.\u00a0Alexander Berkovich, Ali Kemal Uncu. 16 pages.<\/li>\n
  20. arXiv:1510.07301<\/a>\u00a0On partitions with fixed number of even-indexed and odd-indexed odd parts.\u00a0 Alexander Berkovich, Ali Kemal Uncu. 17 pages.<\/li>\n
  21. arXiv:1504.02922<\/a> A New Companion to Capparelli’s Identities. Alexander Berkovich, Ali Kemal Uncu. 9 pages.<\/li>\n
  22. arXiv:1406.7835<\/a>\u00a0On The Gauss EYPHKA Theorem And Some Allied Inequalities. Alexander Berkovich. 12 pages.<\/li>\n
  23. arXiv:1404.2693<\/a>\u00a0Essentially Unique Representations by Certain Ternary Quadratic Forms. Alexander Berkovich, Frank Patane. 20 pages.<\/li>\n
  24. arXiv:1306.5371<\/a>\u00a0A partition inequality involving products of two \\(q\\)-Pochhammer symbols. Alexander Berkovich, Keith Grizzell. 14 pages.<\/li>\n
  25. arXiv:1303.2362<\/a>\u00a0On the class of dominant and subordinate products. Alexander Berkovich, Keith Grizzell. 10 pages.<\/li>\n
  26. arXiv:1302.2359<\/a>\u00a0Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients. Alexander Berkovich, Frank Patane. 23 pages.<\/li>\n
  27. arXiv:1204.1092<\/a>\u00a0On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients. Submitted to arXiv [math.NT]. Alexander Berkovich, Hamza Yesilyurt. 14 pages.<\/li>\n
  28. arXiv:1112.3392<\/a>\u00a0Races among products. Submitted to arXiv [math.NT]. Alexander Berkovich, Keith Grizzell. 9 pages.<\/li>\n
  29. arXiv:1101.2951<\/a>\u00a0On 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.<\/li>\n
  30. arXiv:1010.1926<\/a>\u00a0A proof of the \\(s\\)-genus identities for ternary quadratic forms. Alexander Berkovich, Jonathan Hanke, William Jagy. 14 pages.<\/li>\n
  31. arXiv:0907.1725<\/a>\u00a0On Representation of an Integer by \\(X^2 + Y^2 + Z^2\\) and the Modular Equations of Degree 3 and 5. Alexander Berkovich. 16 pages.<\/li>\n
  32. arXiv:0906.2848<\/a>\u00a0Ternary Quadratic Forms, Modular Equations and Certain Positivity Conjectures. Alexander Berkovich, William Jagy. 24 pages.<\/li>\n
  33. arXiv:0807.4727<\/a>\u00a0The GBG-Rank and \\(t\\)-Cores I. Counting and 4-Cores. Alexander Berkovich, Frank G. Garvan. 15 pages.<\/li>\n
  34. arXiv:0804.2038<\/a>\u00a0On the representations of integers by the sextenary quadratic form \\(x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2\\)\u00a0and 7-cores. Alexander Berkovich, Hamza Yesilyurt. 10 pages.<\/li>\n
  35. An absolute value sum<\/a>,\u00a0American Mathematical Monthly<\/a><\/em>\u00a0115, no. 3 (2008), p. 263. Matthias Beck, Alexander Berkovich.<\/li>\n
  36. arXiv:0801.3008<\/a>\u00a0The tri-pentagonal number theorem and related identities. Alexander Berkovich. 13 pages.<\/li>\n
  37. arXiv:0712.4087<\/a>\u00a0On the difference of partial theta functions. Alexander Berkovich. 6 pages.<\/li>\n
  38. math.NT\/0702027<\/a>\u00a0K. Saito’s Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products. Alexander Berkovich, Frank G. Garvan. 15 pages.<\/li>\n
  39. math.NT\/0611300<\/a>\u00a0Ramanujan’s Identities and Representation of Integers by Certain Binary and Quaternary Quadratic Forms. Alexander Berkovich, Hamza Yesilyurt. 26 pages.<\/li>\n
  40. math.NT\/0603150<\/a>\u00a0New Identities for 7-cores with prescribed BG-rank. Alexander Berkovich, Hamza Yesilyurt. 12 pages.<\/li>\n
  41. math.CO\/0602362<\/a>\u00a0The BG-rank of a partition and its applications. Alexander Berkovich, Frank G. Garvan. 20 pages.<\/li>\n
  42. Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo 6,\u00a0Probability and number theory—Kanazawa 2005,<\/em>\u00a021–39, Adv. Stud. Pure Math., 49,\u00a0Math. Soc. Japan, Tokyo,<\/em>\u00a02007. Krishnaswami Alladi, Alexander Berkovich.<\/li>\n
  43. math.CO\/0409480<\/a>\u00a0Dissecting the Stanley Partition Function. Alexander Berkovich, Frank G. Garvan. 11 pages.<\/li>\n
  44. math.CO\/0403167<\/a>\u00a0Goellnitz-Gordon partitions with weights and parity conditions. Krishnaswami Alladi, Alexander Berkovich. 14 pages.<\/li>\n
  45. math.CO\/0402439<\/a>\u00a0On the Andrews-Stanley Refinement of Ramanujan’s Partition Congruence Modulo 5 and Generalizations. Alexander Berkovich, Frank G. Garvan. 24 pages.<\/li>\n
  46. math.CO\/0302320<\/a>\u00a0Positivity preserving transformations for \\(q\\)-binomial coefficients. Alexander Berkovich, S. Ole Warnaar. 58 pages.<\/li>\n
  47. math.CO\/0205055<\/a>\u00a0A new four parameter q-series identity and its partition implications. Krishnaswami Alladi, George E. Andrews, Alexander Berkovich. 25 pages.<\/li>\n
  48. math.CO\/0205031<\/a>\u00a0A limiting form of the \\(q\\)-Dixon\u00a0\\(_4varphi {}_3\\) summation and related partition identities. Krishnaswami Alladi, Alexander Berkovich. 12 pages.<\/li>\n
  49. math.CO\/0203111<\/a>\u00a0Some Observations on Dyson’s New Symmetries of Partitions. Alexander Berkovich, Frank G. Garvan. 27 pages.<\/li>\n
  50. math.CO\/0203094<\/a>\u00a0New polynomial analogues of Jacobi’s triple product and Lebesgue’s identities. Krishnaswami Alladi, Alexander Berkovich. 19 pages.<\/li>\n
  51. math.CO\/0109141<\/a>\u00a0The WP-Bailey Tree and its Implications. George E. Andrews, Alexander Berkovich. 20 pages.<\/li><\/ol>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":243,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-188","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/pages\/188","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/users\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/comments?post=188"}],"version-history":[{"count":11,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/pages\/188\/revisions"}],"predecessor-version":[{"id":1235,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/pages\/188\/revisions\/1235"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/media?parent=188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}