Bruce A Reznick

If you made any changes in Pure these will be visible here soon.

Research Output

2019

Cantor Set Arithmetic

Athreya, J., Reznick, B. & Tyson, J. T., Jan 2 2019, In : American Mathematical Monthly. 126, 1, p. 4-17 14 p.

Research output: Contribution to journalArticle

Linearly dependent powers of binary quadratic forms

Reznick, B., Jan 1 2019, In : Pacific Journal of Mathematics. 303, 2, p. 729-755 27 p.

Research output: Contribution to journalArticle

On generic and maximal k-ranks of binary forms

Lundqvist, S., Oneto, A., Reznick, B. & Shapiro, B., May 2019, In : Journal of Pure and Applied Algebra. 223, 5, p. 2062-2079 18 p.

Research output: Contribution to journalArticle

2017

Binary forms with three different relative ranks

Reznick, B. & Tokcan, N., Dec 2017, In : Proceedings of the American Mathematical Society. 145, 12, p. 5169-5177 9 p.

Research output: Contribution to journalArticle

The analogue of Hilbert's 1888 theorem for even symmetric forms

Goel, C., Kuhlmann, S. & Reznick, B., Jun 1 2017, In : Journal of Pure and Applied Algebra. 221, 6, p. 1438-1448 11 p.

Research output: Contribution to journalArticle

2016

On the Choi-Lam analogue of Hilbert's 1888 theorem for symmetric forms

Goel, C., Kuhlmann, S. & Reznick, B., May 1 2016, In : Linear Algebra and Its Applications. 496, p. 114-120 7 p.

Research output: Contribution to journalArticle

2013

Congruence Properties of Binary Partition Functions

Anders, K., Dennison, M., Lansing, J. W. & Reznick, B., Feb 11 2013, In : Annals of Combinatorics. 17, 1, p. 15-26 12 p.

Research output: Contribution to journalArticle

On the length of binary forms

Reznick, B., 2013, Quadratic and higher degree forms. Springer New York LLC, Vol. 31. p. 207-232 26 p. (Dev. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

Some new canonical forms for polynomials

Reznick, B., 2013, In : Pacific Journal of Mathematics. 266, 1, p. 185-220 36 p.

Research output: Contribution to journalArticle

2011

Blenders

Reznick, B., 2011, Notions of positivity and the geometry of polynomials. Birkhäuser/Springer Basel AG, Basel, p. 345-373 29 p. (Trends Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

On the sums of two cubes

Reznick, B. & Rouse, J., Nov 1 2011, In : International Journal of Number Theory. 7, 7, p. 1863-1882 20 p.

Research output: Contribution to journalArticle

Pólya's Theorem with zeros

Castle, M., Powers, V. & Reznick, B., Sep 1 2011, In : Journal of Symbolic Computation. 46, 9, p. 1039-1048 10 p.

Research output: Contribution to journalArticle

2010

Laws of inertia in higher degree binary forms

Reznick, B., Mar 1 2010, In : Proceedings of the American Mathematical Society. 138, 3, p. 815-826 12 p.

Research output: Contribution to journalArticle

2009

A quantitative Pólya's Theorem with zeros

Castle, M., Powers, V. & Reznick, B., Sep 1 2009, In : Journal of Symbolic Computation. 44, 9, p. 1285-1290 6 p.

Research output: Contribution to journalArticle

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

Regularity properties of the stern enumeration of the rationals

Reznick, B. A., Sep 16 2008, In : Journal of Integer Sequences. 11, 4, 08.4.1.

Research output: Contribution to journalArticle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1986

Lattice point simplices

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