Leonid N. Vaserstein

    • 1237 Citations
    • 18 h-Index
    1968 …2014
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    Research Output 1968 2014

    • 1237 Citations
    • 18 h-Index
    • 80 Article
    • 1 Review article
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    Article
    2014

    Polynomial parametrization of integer matrices with given determinant

    Gallardo, L. H. & Vaserstein, L. N., Feb 1 2014, In : Journal of Pure and Applied Algebra. 218, 2, p. 321-322 2 p.

    Research output: Contribution to journalArticle

    Integer Matrix
    Square matrix
    Parametrization
    Determinant
    Polynomial

    The stable rank of pullbacks

    Vaserstein, L. N., Jul 15 2014, In : Journal of Algebra. 410, p. 239-243 5 p.

    Research output: Contribution to journalArticle

    Stable Rank
    Pullback
    Ring
    Exceed
    Fiber
    2012
    2 Citations (Scopus)

    Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples

    Frisch, S. & Vaserstein, L., Jan 1 2012, In : Journal of Pure and Applied Algebra. 216, 1, p. 184-191 8 p.

    Research output: Contribution to journalArticle

    Quadruple
    Parametrization
    René Descartes
    Polynomial
    Integer
    2010
    7 Citations (Scopus)

    Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

    Vaserstein, L. N., Jul 6 2010, In : Annals of Mathematics. 171, 2, p. 979-1009 31 p.

    Research output: Contribution to journalArticle

    Arithmetic Groups
    Diophantine equation
    Parametrization
    Polynomial Solutions
    Polynomial
    2 Citations (Scopus)

    Polynomial parametrization of pythagorean tuples

    Vaserstein, L., Sakkalis, T. & Frisch, S., Sep 1 2010, In : International Journal of Number Theory. 6, 6, p. 1261-1272 12 p.

    Research output: Contribution to journalArticle

    Commutative Ring
    Parametrization
    Ring
    Polynomial

    Sums and strict sums of biquadrates in Fq[t],qε{3,9}

    Gallardo, L. H. & Vaserstein, L. N., Dec 1 2010, In : Rocky Mountain Journal of Mathematics. 40, 6, p. 1863-1874 12 p.

    Research output: Contribution to journalArticle

    Biquadrate
    Sum of cubes
    Obstruction
    Congruence
    Polynomial
    2009
    11 Citations (Scopus)

    Non-existence of rational arc length parameterizations for curves in Rn

    Sakkalis, T., Farouki, R. T. & Vaserstein, L. N., Jun 1 2009, In : Journal of Computational and Applied Mathematics. 228, 1, p. 494-497 4 p.

    Research output: Contribution to journalArticle

    Arc length
    Parameterization
    Straight Line
    Nonexistence
    Curve
    13 Citations (Scopus)

    Similarity classes of 3 × 3 matrices over a local principal ideal ring

    Avni, N., Onn, U., Prasad, A. & Vaserstein, L., Aug 1 2009, In : Communications in Algebra. 37, 8, p. 2601-2615 15 p.

    Research output: Contribution to journalArticle

    Ring
    Commutative Ring
    Generating Function
    Quotient
    Similarity
    2008
    4 Citations (Scopus)

    About the period of bell numbers modulo a prime

    Car, M., Gallardo, L. H., Rahavandrainy, O. & Vaserstein, L. N., Jan 1 2008, In : Bulletin of the Korean Mathematical Society. 45, 1, p. 143-155 13 p.

    Research output: Contribution to journalArticle

    Bell numbers
    Irreducible polynomial
    Prime number
    Divides
    Modulo
    8 Citations (Scopus)

    Parametrization of Pythagorean triples by a single triple of polynomials

    Frisch, S. & Vaserstein, L., Jan 1 2008, In : Journal of Pure and Applied Algebra. 212, 1, p. 271-274 4 p.

    Research output: Contribution to journalArticle

    Pythagorean triple
    Parametrization
    Integer-valued Polynomials
    Polynomial
    Integer
    10 Citations (Scopus)

    The strict Waring problem for polynomial rings

    Gallardo, L. H. & Vaserstein, L. N., Dec 1 2008, In : Journal of Number Theory. 128, 12, p. 2963-2972 10 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Polynomial ring
    Polynomial
    2007
    3 Citations (Scopus)

    Representations of polynomials over finite fields of characteristic two as A2 + A + B C + D3

    Gallardo, L., Rahavandrainy, O. & Vaserstein, L. N., Jul 1 2007, In : Finite Fields and their Applications. 13, 3, p. 648-658 11 p.

    Research output: Contribution to journalArticle

    Galois field
    Polynomials
    Polynomial
    Quadratic Polynomial
    Ternary
    2006
    7 Citations (Scopus)

    A note on Bruhat decomposition of GL(n) over local principal ideal rings

    Onn, U., Prasad, A. & Vaserstein, L., Nov 1 2006, In : Communications in Algebra. 34, 11, p. 4119-4130 12 p.

    Research output: Contribution to journalArticle

    Bruhat Decomposition
    Coset
    Ring
    Upper triangular matrix
    Parametrization
    2005
    15 Citations (Scopus)

    On the Whitehead determinant for semi-local rings

    Vaserstein, L. N., Jan 15 2005, In : Journal of Algebra. 283, 2, p. 690-699 10 p.

    Research output: Contribution to journalArticle

    Semilocal Ring
    Multiplicative
    Determinant
    2003
    1 Citation (Scopus)

    Vanishing polynomial sums

    Vaserstein, L. N. & Wheland, E. R., Feb 1 2003, In : Communications in Algebra. 31, 2, p. 751-772 22 p.

    Research output: Contribution to journalArticle

    Polynomial
    Zero
    Univariate
    Multiplicity
    Restriction
    2002
    2 Citations (Scopus)

    On the diophantine equation a3+b3+c3+d3=0

    Gar-El, R. & Vaserstein, L. N., Jan 1 2002, In : Journal of Number Theory. 94, 2, p. 219-223 5 p.

    Research output: Contribution to journalArticle

    Diophantine equation
    2000
    5 Citations (Scopus)

    Quantum (abc)-Theorems

    Vaserstein, L. N., Jan 1 2000, In : Journal of Number Theory. 81, 2, p. 351-358 8 p.

    Research output: Contribution to journalArticle

    Theorem
    2 Citations (Scopus)

    Two-dimensional representations of the free group in two generators over an arbitrary field

    Vaserstein, L. N. & Wheland, E., Mar 1 2000, In : Linear Algebra and Its Applications. 307, 1-3, p. 145-150 6 p.

    Research output: Contribution to journalArticle

    Free Group
    Classify
    Generator
    Arbitrary
    1998
    2 Citations (Scopus)

    Rigid relations in GL2F

    Vaserstein, L. N. & Wheland, E., Sep 15 1998, In : Linear Algebra and Its Applications. 281, 1-3, p. 25-31 7 p.

    Research output: Contribution to journalArticle

    Invertible
    Arbitrary
    1995
    3 Citations (Scopus)

    Commutators in pseudo-orthogonal groups

    Arlinghaus, F. A., Vaserstein, L. N. & You, H., Dec 1995, In : Journal of the Australian Mathematical Society. 59, 3, p. 353-365 13 p.

    Research output: Contribution to journalArticle

    Orthogonal Group
    Commutator
    Stable Rank
    Commutator subgroup
    Unit
    32 Citations (Scopus)

    Normal subgroups of classical groups over rings

    Vaserstein, L. N. & You, H., Nov 24 1995, In : Journal of Pure and Applied Algebra. 105, 1, p. 93-105 13 p.

    Research output: Contribution to journalArticle

    Classical Groups
    Normal subgroup
    Elementary matrix
    Ring
    Orthogonal matrix
    6 Citations (Scopus)

    Products of conjugacy classes of two by two matrices

    Vaserstein, L. N. & Wheland, E., Jan 1 1995, In : Linear Algebra and Its Applications. 230, p. 165-188 24 p.

    Research output: Contribution to journalArticle

    Conjugacy class
    Covering number
    1 Citation (Scopus)

    Products of involutory matrices over rings

    Arlinghaus, F. A., Vaserstein, L. N. & You, H., Nov 1 1995, In : Linear Algebra and Its Applications. 229, C, p. 37-47 11 p.

    Research output: Contribution to journalArticle

    Involution
    Ring
    Commutative Ring
    Express
    Range of data
    1994

    Normal subgroups of classical groups over von neumann regular rings

    Arlinghaus, F. A., Vaserstein, L. N. & You, H., Nov 1 1994, In : Journal of Algebra. 169, 3, p. 863-873 11 p.

    Research output: Contribution to journalArticle

    Von Neumann Regular Ring
    Classical Groups
    Normal subgroup
    Elementary matrix
    Orthogonal matrix
    17 Citations (Scopus)

    On the groups SL2(ℤ[x]) and SL2(k[x, y])

    Grunewald, F., Mennicke, J. & Vaserstein, L., Oct 1 1994, In : Israel Journal of Mathematics. 86, 1-3, p. 157-193 37 p.

    Research output: Contribution to journalArticle

    Quotient
    Galois field
    Subgroup
    1993
    30 Citations (Scopus)

    Isometric embed-dings between classical Banach spaces, cubature formulas, and spherical designs

    Lyubich, Y. I. & Vaserstein, L. N., Sep 1 1993, In : Geometriae Dedicata. 47, 3, p. 327-362 36 p.

    Research output: Contribution to journalArticle

    Spherical Design
    Cubature Formula
    Isometric
    Orbit
    Banach space
    1991

    An improved algorithm for finding saddlepoints of two-person zero-sum games

    Byrne, E. C. C. & Vaserstein, L. N., Jun 1 1991, In : International Journal of Game Theory. 20, 2, p. 149-159 11 p.

    Research output: Contribution to journalArticle

    Two-person Games
    Zero sum game
    Saddlepoint
    Sort
    human being
    1 Citation (Scopus)

    On subgroups of GL2 over Banach algebras and von Neumann regular rings which are normalized by elementary matrices

    Menal, P. & Vaserstein, L. N., Apr 1 1991, In : Journal of Algebra. 138, 1, p. 99-120 22 p.

    Research output: Contribution to journalArticle

    Elementary matrix
    Von Neumann Regular Ring
    Banach algebra
    Subgroup
    Ring
    15 Citations (Scopus)

    On symplectic groups over polynomial rings

    Grunewald, F., Mennicke, J. & Vaserstein, L. N., Jan 1 1991, In : Mathematische Zeitschrift. 206, 1, p. 35-56 22 p.

    Research output: Contribution to journalArticle

    Symplectic Group
    Polynomial ring
    17 Citations (Scopus)

    Sums of cubes in polynomial rings

    Vaserstein, L. N., Jan 1991, In : Mathematics of Computation. 56, 193, p. 349-357 9 p.

    Research output: Contribution to journalArticle

    Sum of cubes
    Polynomial ring
    Regular hexahedron
    Polynomials
    Ring
    1990
    30 Citations (Scopus)

    Commutators and companion matrices over rings of stable rank 1

    Vaserstein, L. N. & Wheland, E., Dec 1990, In : Linear Algebra and Its Applications. 142, C, p. 263-277 15 p.

    Research output: Contribution to journalArticle

    Companion Matrix
    Stable Rank
    Electric commutators
    Commutator
    Ring
    13 Citations (Scopus)

    Factorization of Invertible Matrices Over Rings of Stable Rank One

    Vaserstein, L. N. & Wheland, E., Jun 1990, In : Journal of the Australian Mathematical Society. 48, 3, p. 455-460 6 p.

    Research output: Contribution to journalArticle

    Stable Rank
    Invertible matrix
    Automorphisms
    Factorization
    Ring
    5 Citations (Scopus)

    On the structure of GL2 over stable range one rings

    Menal, P. & Vaserstein, L. N., Jun 12 1990, In : Journal of Pure and Applied Algebra. 64, 2, p. 149-162 14 p.

    Research output: Contribution to journalArticle

    Ring
    Commutative Ring
    Range of data
    Commutativity
    Normal subgroup
    17 Citations (Scopus)

    The subnormal structure of general linear groups over rings

    Vaserstein, L. N., Jan 1 1990, In : Mathematical Proceedings of the Cambridge Philosophical Society. 108, 2, p. 219-229 11 p.

    Research output: Contribution to journalArticle

    General Linear Group
    Ring
    1989
    14 Citations (Scopus)

    Commutators in linear groups

    Dennis, R. K. & Vaserstein, L. N., Nov 1 1989, In : K-Theory. 2, 6, p. 761-767 7 p.

    Research output: Contribution to journalArticle

    Linear Group
    Commutator
    Commutator subgroup
    Natural number
    Automorphism Group
    21 Citations (Scopus)

    Normal subgroups of symplectic groups over rings

    Vaserstein, L. N., Sep 1 1989, In : K-Theory. 2, 5, p. 647-673 27 p.

    Research output: Contribution to journalArticle

    Symplectic Group
    Normal subgroup
    Ring
    Module
    Commutative Ring
    4 Citations (Scopus)

    On subgroups of GL2 over non-commutative local rings which are normalized by elementary matrices

    Menal, P. & Vaserstein, L. N., Oct 1 1989, In : Mathematische Annalen. 285, 2, p. 221-231 11 p.

    Research output: Contribution to journalArticle

    Elementary matrix
    Non-commutative Rings
    Local Ring
    Subgroup
    1988
    25 Citations (Scopus)

    Absolute stable rank and Witt cancellation for noncommutative rings

    Magurn, B. A., Van der Kallen, W. & Vaserstein, L. N., Oct 1 1988, In : Inventiones Mathematicae. 91, 3, p. 525-542 18 p.

    Research output: Contribution to journalArticle

    Stable Rank
    Non-commutative Rings
    Cancellation
    3 Citations (Scopus)

    Every integer is a sum or difference of 28 integral eighth powers

    Vaserstein, L. N., Jan 1 1988, In : Journal of Number Theory. 28, 1, p. 66-68 3 p.

    Research output: Contribution to journalArticle

    Integer
    2 Citations (Scopus)

    Matrix zeros of quadratic equations

    Dafni, G. & Vaserstein, L. N., Jan 1 1988, In : Journal of Number Theory. 30, 1, p. 27-50 24 p.

    Research output: Contribution to journalArticle

    Zero matrix
    Principal ideal domain
    Quadratic equation
    Representation Theory
    Ring
    2 Citations (Scopus)

    Normal subgroups of classical groups over Banach algebras

    Vaserstein, L. N., Dec 1 1988, In : Commentarii Mathematici Helvetici. 63, 1, p. 103-107 5 p.

    Research output: Contribution to journalArticle

    Classical Groups
    Normal subgroup
    Banach algebra
    42 Citations (Scopus)

    On a question of M. Newman on the number of commutators

    Dennis, R. K. & Vaserstein, L. N., Oct 1988, In : Journal of Algebra. 118, 1, p. 150-161 12 p.

    Research output: Contribution to journalArticle

    Commutator
    Euclidean ring
    Commutative Ring
    Ring
    Range of data
    16 Citations (Scopus)
    Homotopy
    Trivial
    Invertible matrix
    Complex Functions
    Topological space
    10 Citations (Scopus)

    Subnormal structure of the general linear groups over Banach algebras

    Vaserstein, L. N., May 1988, In : Journal of Pure and Applied Algebra. 52, 1-2, p. 187-195 9 p.

    Research output: Contribution to journalArticle

    General Linear Group
    Banach algebra
    Ring
    Subgroup
    Elementary matrix
    1987
    11 Citations (Scopus)

    Computation of k1via mennicke symbols

    Vaserstein, L. N., Jan 1987, In : Communications in Algebra. 15, 3, p. 611-656 46 p.

    Research output: Contribution to journalArticle

    Rings of Continuous Functions
    Ring
    Invertible matrix
    Krull Dimension
    Generalise
    9 Citations (Scopus)

    On The Sum Of Powers Of Matrices

    Vaserstein, L. N., Nov 1 1987, In : Linear and Multilinear Algebra. 21, 3, p. 261-270 10 p.

    Research output: Contribution to journalArticle

    Sums of Powers
    Sum of squares
    Ring
    Algebraic number Field
    Question Answering
    2 Citations (Scopus)

    Prestabilization for K1 of banach algebras

    Vaserstein, L. N. & Magurnt, B. A., Oct 1987, In : Linear Algebra and Its Applications. 95, C, p. 69-96 28 p.

    Research output: Contribution to journalArticle

    Banach algebra
    Algebra
    Elementary matrix
    kernel
    Electric commutators
    20 Citations (Scopus)

    Waring's problem for algebras over fields

    Vaserstein, L. N., Jul 1987, In : Journal of Number Theory. 26, 3, p. 286-298 13 p.

    Research output: Contribution to journalArticle

    Waring's problem
    Algebra
    1986
    4 Citations (Scopus)

    An answer to a question of M. Newman on matrix completion

    Vaserstein, L. N., Jan 1 1986, In : Proceedings of the American Mathematical Society. 97, 2, p. 189-196 8 p.

    Research output: Contribution to journalArticle

    Matrix Completion
    Ring
    Commutative Ring
    Determinant
    Theorem
    8 Citations (Scopus)

    Every Integral Matrix is the Sum of Three Squares

    Vaserstein, L. N., Nov 1 1986, In : Linear and Multilinear Algebra. 20, 1, p. 1-4 4 p.

    Research output: Contribution to journalArticle

    Ring