Berkovich, Alexander

• 2843310
  Berkovich, Alexander(1-FL); Jagy, William C.(1-MSRI)
  On representation of an integer as the sum of three squares and ternary quadratic forms with the discriminants $p^2$$p^2$, $16p^2$$16p^2$. (English summary)
  J. Number Theory 132 (2012), no. 1, 258–274.
  11E20 (05A19 05A30 11B65 11F37 33E05)
  
• 2744264
  Berkovich, Alexander(1-FL); Jagy, William C.(1-MSRI)
  Ternary quadratic forms, modular equations, and certain positivity conjectures. (English summary) The legacy of Alladi Ramakrishnan in the mathematical sciences, 211–241, Springer, New York, 2010.
  11E20 (05A30 11B65 11F37 33D15)
  
• 2681308
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  The GBG-rank and $t$$t$-cores I. Counting and 4-cores. (English summary)
  J. Comb. Number Theory 1 (2009), no. 3, 237–252.
  11P81 (05A17 11P83 33D15)
  
• 2582981
  Berkovich, Alexander(1-FL)
  The tri-pentagonal number theorem and related identities. (English summary)
  Int. J. Number Theory 5 (2009), no. 8, 1385--1399.
  33D15 (11B65)
  
• 2574780
  Berkovich, Alexander(1-FL); Yesilyurt, Hamza(TR-BILK)
  Ramanujan's identities and representation of integers by certain binary and quaternary quadratic forms. (English summary)
  Ramanujan J. 20 (2009), no. 3, 375--408.
  11E16 (11E25 11F27 11F30 33D15)
  
• 2521479
  Berkovich, Alexander(1-FL); Yesilyurt, Hamza(TR-BILK)
  On the representations of integers by the sextenary quadratic form $x\sp 2+y\sp 2+z\sp 2+7s\sp 2+7t\sp 2+7u\sp 2$ and 7-cores. (English summary)
  J. Number Theory 129 (2009), no. 6, 1366--1378.
  11F27 (11P82)
  
• 2450458
  Berkovich, Alexander(1-FL); Yesilyurt, Hamza(TR-BILKS)
  New identities for 7-cores with prescribed BG-rank. (English summary)
  Discrete Math. 308 (2008), no. 22, 5246--5259.
  05A20 (05A19 11P82)
  
• 2419190
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  K. Saito's conjecture for nonnegative eta products and analogous results for other infinite products. (English summary)
  J. Number Theory 128 (2008), no. 6, 1731--1748.
  11F20 (11B65 11F27 33D15)
  
• 2402176
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  The BG-rank of a partition and its applications. (English summary)
  Adv. in Appl. Math. 40 (2008), no. 3, 377--400.
  11P81 (05A17 05A19 11P83)
  
• 2405596
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo 6. (English summary) Probability and number theory---Kanazawa 2005, 21--39,
  Adv. Stud. Pure Math., 49, Math. Soc. Japan, Tokyo, 2007.
  11P83 (05A17 05A19 33D15)
  
• 2177037
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo 5 and generalizations. (English. English summary)
  Trans. Amer. Math. Soc. 358 (2006), no. 2, 703--726 (electronic).
  05A17 (11P81 11P83)
• 2179269
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  Göllnitz-Gordon partitions with weights and parity conditions. (English. English summary)
  Zeta functions, topology and quantum physics, 1--17,
  Dev. Math., 14,
  Springer, New York, 2005.
  05A17 (05A30 11P83 33D15)
• 2177487
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  Dissecting the Stanley partition function. (English. English summary)
  J. Combin. Theory Ser. A 112 (2005), no. 2, 277--291.
  05A17 (11Pxx)
• 2140441
  Berkovich, Alexander(1-FL); Warnaar, S. Ole(5-MELB-MS)
  Positivity preserving transformations for $q$-binomial coefficients. (English. English summary)
  Trans. Amer. Math. Soc. 357 (2005), no. 6, 2291--2351 (electronic).
  33D15 (05E05 33C20)
• 2063196
  Alladi, K.(1-FL); Andrews, G. E.(1-PAS); Berkovich, A.(1-FL)
  A four parameter generalization of Göllnitz's (big) partition theorem. (English. English summary)
  Unusual applications of number theory, 1--7,
  DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 64,
  Amer. Math. Soc., Providence, RI, 2004.
  11P81 (05A15 05A17 11P83 33D15)
• 2053846
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  New polynomial analogues of Jacobi's triple product and Lebesgue's identities. (English. English summary)
  Adv. in Appl. Math. 32 (2004), no. 4, 801--824.
  33D45 (11B65 11P81)
• 1992013
  Alladi, Krishnaswami(1-FL); Andrews, George E.(1-PAS); Berkovich, Alexander(1-FL)
  A new four parameter $q$-series identity and its partition implications. (English. English summary)
  Invent. Math. 153 (2003), no. 2, 231--260.
  05A30 (05A17 11B65 11P83 33D15)
• 1974131
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  A limiting form of the $q$-Dixon $\sb 4\phi\sb 3$ summation and related partition identities. (English. English summary)
  Number theoretic methods (Iizuka, 2001), 1--14,
  Dev. Math., 8,
  Kluwer Acad. Publ., Dordrecht, 2002.
  11P83 (33D15)
• 1934290
  Andrews, George(1-PAS); Berkovich, Alexander(1-FL)
  The WP-Bailey tree and its implications. (English. English summary)
  J. London Math. Soc. (2) 66 (2002), no. 3, 529--549.
  33D15 (05A19 05A30 11B65)
• 1932070
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  Some observations on Dyson's new symmetries of partitions. (English. English summary)
  J. Combin. Theory Ser. A 100 (2002), no. 1, 61--93.
  11P81 (05A17 05A19)
• 1909082
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  A double bounded version of Schur's partition theorem. (English. English summary)
  Special issue: Paul Erdös and his mathematics.
  Combinatorica 22 (2002), no. 2, 151--168.
  11P83 (05A17 05A19 11P81)
• 1895193
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  New weighted Rogers-Ramanujan partition theorems and their implications. (English. English summary)
  Trans. Amer. Math. Soc. 354 (2002), no. 7, 2557--2577 (electronic).
  11P83 (05A17 05A19)
• 1884385
  Berkovich, Alexander(1-PAS); Riese, Axel(A-LINZ-SC)
  A computer proof of a polynomial identity implying a partition theorem of Göllnitz. (English. English summary)
  Adv. in Appl. Math. 28 (2002), no. 1, 1--16.
  05A19
• 1891420
  Berkovich, Alexander(1-FL); Paule, Peter(A-LINZ-SC)
  Variants of the Andrews-Gordon identities. (English. English summary)
  Ramanujan J. 5 (2001), no. 4, 391--404 (2002).
  11P82 (05A19 11P81)
• 1891414
  Berkovich, Alexander(1-FL); Paule, Peter(A-LINZ-SC)
  Lattice paths, $q$-multinomials and two variants of the Andrews-Gordon identities. (English. English summary)
  Ramanujan J. 5 (2001), no. 4, 409--425 (2002).
  11B65 (05A19 05A30 11P82)
• 1880077
  Alladi, Krishnaswami(1-FL); Berkovich, Alexander(1-FL)
  A double bounded key identity for Göllnitz's (big) partition theorem. (English. English summary)
  Symbolic computation, number theory, special functions, physics and combinatorics (Gainesville, FL, 1999), 13--32,
  Dev. Math., 4,
  Kluwer Acad. Publ., Dordrecht, 2001.
  11P81 (05A17 05A19 33D15)
• 1811903
  Berkovich, Alexander(1-SUNYS-T); McCoy, Barry M.(1-SUNYS-T)
  The perturbation $\phi\sb {2,1}$ of the $M(p,p+1)$ models of conformal field theory and related polynomial-character identities. (English. English summary)
  Ramanujan J. 4 (2000), no. 4, 353--383.
  81T40 (05A19 05A30 11B65 11P81 82B23)
• 1704005
  Berkovich, Alexander(1-SUNYS-IT); McCoy, Barry M.(1-SUNYS-IT)
  The universal chiral partition function for exclusion statistics. (English. English summary)
  Statistical physics on the eve of the 21st century, 240--256,
  Ser. Adv. Statist. Mech., 14,
  World Sci. Publishing, River Edge, NJ, 1999.
  81S05 (81R12 81T40 82B10)
• 1648151
  Berkovich, Alexander(1-SUNYS-IT); McCoy, Barry M.(1-SUNYS-IT)
  Rogers-Ramanujan identities: a century of progress from mathematics to physics. (English. English summary)
  Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998).
  Doc. Math. 1998, Extra Vol. III, 163--172 (electronic).
  11P82 (01A60 11-03 82B23)
• 1627553
  Berkovich, Alexander(1-SUNYS-T); McCoy, Barry M.(1-SUNYS-T); Pearce, Paul A.(5-MELB-MS)
  The perturbations $\phi\sb {2,1}$ and $\phi\sb {1,5}$ of the minimal models $M(p,p')$ and the trinomial analogue of Bailey's lemma. (English. English summary)
  Nuclear Phys. B 519 (1998), no. 3, 597--625.
  81T40 (11P82)
• 1617566
  Andrews, G. E.(1-PAS); Berkovich, A.(1-PAS)
  A trinomial analogue of Bailey's lemma and $N=2$ superconformal invariance. (English. English summary)
  Comm. Math. Phys. 192 (1998), no. 2, 245--260.
  11P82 (05A30 33D80 81T40)
• 1604352
  Berkovich, Alexander(D-BONN-P); McCoy, Barry M.(1-SUNYS-IT); Schilling, Anne(1-SUNYS-IT)
  Rogers-Schur-Ramanujan type identities for the $M(p,p')$ minimal models of conformal field theory. (English. English summary)
  Comm. Math. Phys. 191 (1998), no. 2, 325--395.
  81R10 (11B65 11Z05 81T40 82B23)
• 1492500
  Berkovich, A.(D-BONN-P); McCoy, B. M.(1-SUNYS-T)
  Generalizations of the Andrews-Bressoud identities for the $N=1$ superconformal model ${\rm SM}(2,4\nu)$. (English. English summary)
  Combinatorics and physics (Marseilles, 1995).
  Math. Comput. Modelling 26 (1997), no. 8-10, 37--49.
  11P82 (11B65 33D20 81T40 82B23)
• 1476630
  Berkovich, Alexander(1-PAS); McCoy, Barry M.(1-SUNYS-IT); Schilling, Anne(1-SUNYS-IT); Warnaar, S. Ole(5-MELB)
  Bailey flows and Bose-Fermi identities for the conformal coset models $(A\sp {(1)}\sb 1)\sb N\times(A\sp {(1)}\sb 1)\sb {N'}/(A\sp {(1)}\sb 1)\sb {N+N'}$. (English. English summary)
  Nuclear Phys. B 499 (1997), no. 3, 621--649.
  81R10 (81T40)
• 1399281
  Berkovich, Alexander(D-BONN-P); McCoy, Barry M.(1-SUNYS-IT); Schilling, Anne(1-SUNYS-IT)
  $N=2$ supersymmetry and Bailey pairs. (English. English summary)
  Phys. A 228 (1996), no. 1-4, 33--62.
  81R10 (11B65 33D15 81T40 82B23)
• 1392146
  Berkovich, Alexander(D-BONN-P); McCoy, Barry M.(1-SUNYS-IT)
  Continued fractions and fermionic representations for characters of $M(p,p')$ minimal models. (English. English summary)
  Lett. Math. Phys. 37 (1996), no. 1, 49--66.
  81R10 (11B65 11P83 81T40 82B23)
• 1392415
  Berkovich, Alexander(D-BONN-P); McCoy, Barry M.(1-SUNYS-IT); Orrick, William P.(1-SUNYS-IT)
  Polynomial identities, indices, and duality for the $N=1$ superconformal model $SM(2,4\nu)$. (English. English summary)
  J. Statist. Phys. 83 (1996), no. 5-6, 795--837.
  82B23 (11P82 17B68 33D90)
• 1305107
  Berkovich, Alexander(D-BONN-P)
  Fermionic counting of RSOS states and Virasoro character formulas for the unitary minimal series $M(\nu,\nu+1)$: exact results. (English. English summary)
  Nuclear Phys. B 431 (1994), no. 1-2, 315--348.
  81R10 (17B68 33D05 82B23)
• 1267014
  Berkovich, Alexander(E-CSIC); Gómez, César(E-CSIC); Sierra, Germán(E-CSIC)
  Spin-anisotropy commensurable chains. Quantum group symmetries and $N=2$ SUSY. (English. English summary)
  Nuclear Phys. B 415 (1994), no. 3, 681--733.
  82B23 (81-02 81R50 82-02)
• 1210712
  Berkovich, Alexander(E-CSIC); Gómez, César(CH-GENV-P); Sierra, Germán(E-CSIC)
  $q$-magnetism at roots of unity. (English. English summary)
  J. Phys. A 26 (1993), no. 2, L45--L51.
  82B20 (81R50 82B23)
• 1186853
  Berkovich, Alexander(E-CSIC-FP); Gómez, César(E-CSIC-FP); Sierra, Germán(E-CSIC-FP)
  On a new class of integrable models.
  Topological and quantum group methods in field theory and condensed matter physics.
  Internat. J. Modern Phys. B 6 (1992), no. 11-12, 1939--1950.
  82B23 (17B37)
• 1121825
  Berkovich, Alexander(1-NY-P)
  Temperature and magnetic field-dependent correlators of the exactly integrable $(1+1)$-dimensional gas of impenetrable fermions.
  J. Phys. A 24 (1991), no. 7, 1543--1556.
  82B10 (82B20)
• 1121824
  Berkovich, Alexander(1-SUNYS-T); Murthy, Ganpathy(1-SUNYS-T)
  Current correlations in the nonlinear Schrödinger model from conformal field theory.
  J. Phys. A 24 (1991), no. 7, 1537--1542.
  81T40 (81R10 82B10)
• 1115849
  Berkovich, A.(1-SUNYS-T)
  Conformal invariance, finite-size effects, and the exact correlators for the $\delta$-function Bose gas.
  Nuclear Phys. B 356 (1991), no. 3, 655--684.
  81T40
• 1030942
  Berkovich, A.(1-SUNYS-T); Murthy, G.(1-SUNYS-T)
  Time-dependent multipoint correlation functions of the nonlinear Schrödinger model.
  Phys. Lett. A 142 (1989), no. 2-3, 121--127.
  81T10
• 968306
  Berkovich, A.(1-SUNYS-T); Murthy, G.(1-SUNYS-T)
  Operator dimensions and surface exponents for the nonlinear Schrödinger model at $T=0$.
  J. Phys. A 21 (1988), no. 19, 3703--3721.
  81E99 (81E40)
• 951036
  Berkovich, A.(1-SUNYS-T); Murthy, Ganpathy(1-SUNYS-T)
  Finite-size corrections in the nonlinear Schrödinger model.
  J. Phys. A 21 (1988), no. 7, L395--L400.
  82A05 (81E40 82A69)
• 891832
  Berkovich, A.(1-NY-P); Lowenstein, J. H.(1-NY-P)
  Correlation function of the one-dimensional Fermi gas in the infinite-coupling limit (repulsive case).
  Nuclear Phys. B 285 (1987), no. 1, 70--96.
  82A15