Berkovich, Alexander

62 papers

3861706
Berkovich, Alex(1-FL)

Department of Mathematics, University of Florida
Gainesville, Florida, 32611 ; Chan, Heng Huat(SGP-SING)

Department of Mathematics, National University of Singapore
Kent Ridge, Singapore 0511, Singapore ; Schlosser, Michael J.(A-WIENM)

Universität Wien
1090 Vienna, Austria
Wronskians of theta functions and series for $1/\pi$ $1/\pi$ . (English summary)
Adv. Math. 338 (2018), 266-304.
11F11 (11F20 11F27 11Y60)

3787346
Berkovich, Alexander; Uncu, Ali Kemal
On some polynomials and series of Bloch-Pólya type.
Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827-2838.
05A17 (05A19 05A30 11B65 11P81)

3622129
Berkovich, Alexander(1-FL)

Department of Mathematics, University of Florida
Gainesville, Florida, 32611 ; Uncu, Ali K.(1-FL)

Department of Mathematics, University of Florida
Gainesville, Florida, 32611
Variation on a theme of Nathan Fine. New weighted partition identities. (English summary)
J. Number Theory 176 (2017), 226-248.
05A17 (05A19 05E10 11B34 11B75 11P81 11P84 33D15)

3504032
Berkovich, Alexander(1-FL); Uncu, Ali Kemal(1-FL)
On partitions with fixed number of even-indexed and odd-indexed odd parts. (English summary)
J. Number Theory 167 (2016), 7-30.
11P83 (05A15 05A17 05A19 11B34 11B37 11B75 11P81)

3406960
Berkovich, Alexander(1-FL); Uncu, Ali Kemal(1-FL)
A new companion to Capparelli's identities. (English summary)
Adv. in Appl. Math. 71 (2015), 125-137.
05A19 (05A15 05A17 05A20 11P83)

3305036
Berkovich, Alexander(1-FL); Patane, Frank(1-FL)
Essentially unique representations by certain ternary quadratic forms. (English summary)
Exp. Math. 24 (2015), no. 1, 8-22.
11E25 (11B65 11E16 11E20 11E41 11F37)

3283163
Berkovich, Alexander(1-FL)
On the Gauss $E\Upsilon PHKA$ $E\Upsilon PHKA$ theorem and some allied inequalities. (English summary)
J. Number Theory 148 (2015), 1-18.
11B65 (11E12 11E16 11E20 11E25 11E41 11F37)

3148513
Berkovich, Alexander(1-FL); Yesilyurt, Hamza(TR-BILK)
On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients. (English summary)
Proc. Amer. Math. Soc. 142 (2014), no. 3, 777–793.
11E16 (11E45 11F03)

3128458
Berkovich, Alexander(1-FL); Patane, Frank(1-FL)
Binary quadratic forms and the Fourier coefficients of certain weight 1 $eta$ $eta$ -quotients. (English summary)
J. Number Theory 135 (2014), 185–220.
11B65 (11F03 11F27 14K25)

3156553
Berkovich, Alexander(1-FL)
On representation of an integer by $X^2+Y^2+Z^2$ $X^2+Y^2+Z^2$ and the modular equations of degree 3 and 5. (English summary) Quadratic and higher degree forms, 29–49,
Dev. Math., 31, Springer, New York, 2013.
11E20 (05A30 11F37 33E05)

2994111
Berkovich, Alexander(1-FL); Hanke, Jonathan(1-GA); Jagy, Will(1-MSRI)
A proof of the $S$ $S$ -genus identities for ternary quadratic forms. (English summary)
Ramanujan J. 29 (2012), no. 1-3, 431–445.
11E12 (11E20 11E25 11F27 11F30)

2946386
Berkovich, Alexander(1-FL); Grizzell, Keith(1-FL)
Races among products. (English summary)
J. Combin. Theory Ser. A 119 (2012), no. 8, 1789–1797.
05A17 (05A15 05A20)

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