Bruce A Reznick

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Research Output

1974

A uniqueness criterion for fractional iteration

Reznick, B. A., 1974, In : Annales Polonici Mathematici. 30, p. 219-224 6 p.

Research output: Contribution to journalArticle

Problems and Solutions: Elementary Problems: E2480-E2485

Klamkin, M. S., Reznick, B., Ruderman, H. D., Forsey, H. & Eddy, R. H., 1974, In : American Mathematical Monthly. 81, 6, p. 659-660 2 p.

Research output: Contribution to journalArticle

1978

Banach spaces which satisfy linear identities

Reznick, B., Jan 1978, In : Pacific Journal of Mathematics. 74, 1, p. 221-234 14 p.

Research output: Contribution to journalArticle

Open Access

Extremal PSD forms with few terms

Reznick, B., Jun 1978, In : Duke Mathematical Journal. 45, 2, p. 363-374 12 p.

Research output: Contribution to journalArticle

1979

Banach spaces with polynomial norms

Reznick, B., May 1979, In : Pacific Journal of Mathematics. 82, 1, p. 223-235 13 p.

Research output: Contribution to journalArticle

When is the Iterate of A Formal Power Series Odd?

Reznick, B. A., Jan 1 1979, In : Journal of the Australian Mathematical Society. 28, 1, p. 62-66 5 p.

Research output: Contribution to journalArticle

1980

Real zeros of positive semidefinite forms. I

Choi, M. D., Lam, T. Y. & Reznick, B. A., Feb 1 1980, In : Mathematische Zeitschrift. 171, 1, p. 1-26 26 p.

Research output: Contribution to journalArticle

Sums of squares in some integral domains

Choi, M. D., Lam, T. Y., Reznick, B. & Rosenberg, A., Jul 1980, In : Journal of Algebra. 65, 1, p. 234-256 23 p.

Research output: Contribution to journalArticle

1981

A Turán inequality arising in information theory

McEliece, R. J., Reznick, B. & Shearer, J. B., 1981, In : SIAM Journal on Mathematical Analysis. 12, 6, p. 931-934 4 p.

Research output: Contribution to journalArticle

1982

The Pythagoras number of some affine algebras and local algebras

Choi, M. D., Dai, Z. D., Lam, T. Y. & Reznick, B., Jan 1 1982, In : Journal fur die Reine und Angewandte Mathematik. 1982, 336, p. 45-82 38 p.

Research output: Contribution to journalArticle

Transversal zeros and positive semidefinite forms

Choi, M. D., Knebusch, M., Lam, T. Y. & Reznick, B., 1982, Real algebraic geometry and quadratic forms (Rennes, 1981). Springer, Berlin-New York, Vol. 959. p. 273-298 26 p. (Lecture Notes in Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

1983

Continued fractions and an annelidic PDE

Reznick, B., Dec 1 1983, In : The Mathematical Intelligencer. 5, 4, p. 61-63 3 p.

Research output: Contribution to journalArticle

On elementary methods in positivity theory

Gillis, J., Reznick, B. & Zeilberger, D., 1983, In : SIAM Journal on Mathematical Analysis. 14, 2, p. 396-398 3 p.

Research output: Contribution to journalArticle

Skewness in banach spaces

Fitzpatrick, S. & Reznick, B. A., Feb 1983, In : Transactions of the American Mathematical Society. 275, 2, p. 587-597 11 p.

Research output: Contribution to journalArticle

Some inequalities for products of power sums

Reznick, B., Feb 1983, In : Pacific Journal of Mathematics. 104, 2, p. 443-463 21 p.

Research output: Contribution to journalArticle

1985

Decomposition of product graphs into complete bipartite subgraphs

Reznick, B., Tiwari, P. & West, D. B., Nov 1985, In : Discrete Mathematics. 57, 1-2, p. 189-193 5 p.

Research output: Contribution to journalArticle

Some extremal problems for continued fractions

Reznick, B. A., Jan 1 1985, In : Illinois Journal of Mathematics. 29, 2, p. 261-279 19 p.

Research output: Contribution to journalArticle

1986

Lattice point simplices

Reznick, B., Jan 1 1986, In : Discrete Mathematics. 60, C, p. 219-242 24 p.

Research output: Contribution to journalArticle

1987

A quantitative version of Hurwitz' theorem on the arithmetic-geometric inequality

Reznick, B., Jan 1 1987, In : Journal fur die Reine und Angewandte Mathematik. 1987, 377, p. 108-112 5 p.

Research output: Contribution to journalArticle

Even symmetric sextics

Choi, M. D., Lam, T. Y. & Reznick, B., Dec 1 1987, In : Mathematische Zeitschrift. 195, 4, p. 559-580 22 p.

Research output: Contribution to journalArticle

The asymptotic behavior of a family of sequences

Erdös, P., Hildebrand, A., Odlyzko, A., Pudaite, P. & Reznick, B., Feb 1987, In : Pacific Journal of Mathematics. 126, 2, p. 227-241 15 p.

Research output: Contribution to journalArticle

1988

Eigensharp graphs:Decomposition into complete bipartite subgraphs

Kratzke, T., Reznick, B. & West, D., Aug 1988, In : Transactions of the American Mathematical Society. 308, 2, p. 637-653 17 p.

Research output: Contribution to journalArticle

1989

Digital representations using the greatest integer function

Reznick, B. A., Mar 1989, In : Transactions of the American Mathematical Society. 312, 1, p. 355-375 21 p.

Research output: Contribution to journalArticle

Forms derived from the arithmetic-geometric inequality

Reznick, B. A., Sep 1 1989, In : Mathematische Annalen. 283, 3, p. 431-464 34 p.

Research output: Contribution to journalArticle

The sum of the squares of the parts of a partition, and some related questions

Reznick, B., Oct 1989, In : Journal of Number Theory. 33, 2, p. 199-208 10 p.

Research output: Contribution to journalArticle

1990

Some binary partition functions

Reznick, B., 1990, Analytic number theory (Allerton Park, IL, 1989). Birkhäuser Boston, Boston, MA, Vol. 85. p. 451-477 27 p. (Progr. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

1991

Positive sextics and Schur's inequalities

Choi, M. D., Lam, T. Y. & Reznick, B., Aug 1 1991, In : Journal of Algebra. 141, 1, p. 36-77 42 p.

Research output: Contribution to journalReview article

1992

Sums of even powers of real linear forms

Reznick, B., 1992, In : Memoirs of the American Mathematical Society. 96, 463, p. viii+155

Research output: Contribution to journalArticle

1993

An inequality for products of polynomials

Reznick, B., 1993, In : Proceedings of the American Mathematical Society. 117, 4, p. 1063-1073 11 p.

Research output: Contribution to journalArticle

1995

Some constructions of spherical 5-designs

Reznick, B., 1995, In : Linear Algebra and Its Applications. 226-228, C, p. 163-196 34 p.

Research output: Contribution to journalArticle

Sums of squares of real polynomials

Choi, M. D., Lam, T. Y. & Reznick, B., 1995, $K$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992). Amer. Math. Soc., Providence, R.I., Vol. 58. p. 103-126 24 p. (Proc. Sympos. Pure Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

Uniform denominators in Hilbert's seventeenth problem

Reznick, B. A., Dec 1 1995, In : Mathematische Zeitschrift. 220, 1, p. 75-97 23 p.

Research output: Contribution to journalArticle

1996

Homogeneous polynomial solutions to constant coefficient PDE's

Reznick, B., Feb 10 1996, In : Advances in Mathematics. 117, 2, p. 179-192 14 p.

Research output: Contribution to journalArticle

Sums of 2m-th powers of rational functions in one variable over real closed fields

Choi, M. D., Lam, T. Y., Prestel, A. & Reznick, B., Jan 1996, In : Mathematische Zeitschrift. 221, 1, p. 93-112 20 p.

Research output: Contribution to journalArticle

1998

The maximal angular gap among rectangular grid points

Füredi, Z. & Reznick, B., 1998, In : Periodica Mathematica Hungarica. 36, 2-3, p. 119-137 19 p.

Research output: Contribution to journalArticle

1999

On the Nonmonotonicity of (Im(zn))

Reznick, B., Sep 1 1999, In : Journal of Number Theory. 78, 1, p. 144-148 5 p.

Research output: Contribution to journalArticle

2000

Notes towards a constructive proof of Hilbert's theorem on ternary quartics

Powers, V. & Reznick, B., 2000, Quadratic forms and their applications (Dublin, 1999). Amer. Math. Soc., Providence, R.I., Vol. 272. p. 209-227 19 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

Polynomials that are positive on an interval

Powers, V. & Reznick, B., 2000, In : Transactions of the American Mathematical Society. 352, 10, p. 4677-4692 16 p.

Research output: Contribution to journalArticle

Open Access

Some concrete aspects of Hilbert's 17th Problem

Reznick, B., 2000, Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996). Amer. Math. Soc., Providence, R.I., Vol. 253. p. 251-272 22 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

2001

A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra

Powers, V. & Reznick, B., Oct 24 2001, In : Journal of Pure and Applied Algebra. 164, 1-2, p. 221-229 9 p.

Research output: Contribution to journalArticle

2002

Lattice polytopes with distinct pair-sums

Choi, M. D., Lam, T. Y. & Reznick, B., Jan 2002, In : Discrete and Computational Geometry. 27, 1, p. 65-72 8 p.

Research output: Contribution to journalArticle

2003

Patterns of dependence among powers of polynomials

Reznick, B., 2003, Algorithmic and quantitative real algebraic geometry (Piscataway, NJ, 2001). Amer. Math. Soc., Providence, R.I., Vol. 60. p. 101-121 21 p. (DIMACS Ser. Discrete Math. Theoret. Comput. Sci.).

Research output: Chapter in Book/Report/Conference proceedingChapter

2004

A new approach to Hilbert's theorem on ternary quartics

Powers, V., Reznick, B., Scheiderer, C. & Sottile, F., Nov 1 2004, In : Comptes Rendus Mathematique. 339, 9, p. 617-620 4 p.

Research output: Contribution to journalArticle

Positive Rational Solutions to xy = ymx: A Number-Theoretic Excursion

Bennett, M. A. & Reznick, B., Jan 2004, In : American Mathematical Monthly. 111, 1, p. 13-21 9 p.

Research output: Contribution to journalArticle

2005

On the absence of uniform denominators in Hilbert's 17th problem

Reznick, B., Oct 2005, In : Proceedings of the American Mathematical Society. 133, 10, p. 2829-2834 6 p.

Research output: Contribution to journalArticle

Polynomials positive on unbounded rectangles

Powers, V. & Reznick, B., Jan 1 2005, In : Lecture Notes in Control and Information Sciences. 312, p. 151-163 13 p.

Research output: Contribution to journalArticle

Problems from the Cottonwood Room

Beck, M., Chen, B., Fukshansky, L., Haase, C., Knutson, A., Reznick, B., Robins, S. & Schürmann, A., 2005, Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics. Amer. Math. Soc., Providence, R.I., Vol. 374. p. 179-191 13 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

2006

Almost alternating sums

O'Bryant, K., Reznick, B. & Serbinowska, M., Oct 2006, In : American Mathematical Monthly. 113, 8, p. 673-688 16 p.

Research output: Contribution to journalArticle

A quantitative Pólya's theorem with corner zeros

Powers, V. & Reznick, B., 2006, Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ISSAC 2006. Association for Computing Machinery (ACM), p. 285-289 5 p. (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; vol. 2006).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2008

Let me tell you my favorite lattice-point problem. . .

Beck, M., Nill, B., Reznick, B., Savage, C., Soprunov, I. & Xu, Z., 2008, Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics. Amer. Math. Soc., Providence, R.I., Vol. 452. p. 179-187 9 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter