Bruce Reznick

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All published works

Action	Title	Year	Authors
+	Equal sums of two cubes of quadratic forms	2024	Bruce Reznick
+ PDF Chat	On odd powers of nonnegative polynomials that are not sums of squares	2024	Grigoriy Blekherman Khazhgali Kozhasov Bruce Reznick
+ PDF Chat	Sums of squares of k-term forms	2024	Charu Goel Bruce Reznick
+	Representations of integers as quotients of sums of distinct powers of three	2023	Katie Anders Madeline Locus Dawsey Bruce Reznick Simone Sisneros-Thiry
+ PDF Chat	Sparse versions of the Cayley–Bacharach theorem	2021	Laura Felicia Matusevich Bruce Reznick
+	Equal sums of two cubes of quadratic forms	2020	Bruce Reznick
+	A note on mediated simplices	2020	Victoria Powers Bruce Reznick
+	Equal sums of two cubes of binary quadratic forms	2020	Bruce Reznick
+ PDF Chat	Linearly dependent powers of binary quadratic forms	2019	Bruce Reznick
+	Sparse Versions of the Cayley-Bacharach Theorem	2019	Laura Felicia Matusevich Bruce Reznick
+	Cantor Set Arithmetic	2019	Jayadev S. Athreya Bruce Reznick Jeremy T. Tyson
+	A note on mediated simplices	2019	Victoria Powers Bruce Reznick
+	Sparse Versions of the Cayley-Bacharach Theorem	2019	Laura Felicia Matusevich Bruce Reznick
+ PDF Chat	On generic and maximal k-ranks of binary forms	2018	Samuel Lundqvist Alessandro Oneto Bruce Reznick Boris Shapiro
+	Cantor set arithmetic	2017	Jayadev S. Athreya Bruce Reznick Jeremy T. Tyson
+ PDF Chat	On generic and maximal $k$-ranks of binary forms	2017	Samuel Lundqvist Alessandro Oneto Bruce Reznick Boris Shapiro
+	Binary forms with three different relative ranks	2017	Bruce Reznick Neriman Tokcan
+	Cantor set arithmetic	2017	Jayadev S. Athreya Bruce Reznick Jeremy T. Tyson
+ PDF Chat	The analogue of Hilbert's 1888 theorem for even symmetric forms	2016	Charu Goel Salma Kuhlmann Bruce Reznick
+	Binary forms with three different relative ranks	2016	Bruce Reznick Neriman Tokcan
+	On the Choi–Lam analogue of Hilbert's 1888 theorem for symmetric forms	2016	Charu Goel Salma Kuhlmann Bruce Reznick
+	Binary forms with three different relative ranks	2016	Bruce Reznick Neriman Tokcan
+	On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms	2015	Charu Goel Salma Kuhlmann Bruce Reznick
+	On the analogue of Hilbert's 1888 Theorem for Symmetric and Even Symmetric Forms	2015	Charu Goel Salma Kuhlmann Bruce Reznick
+	On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms	2015	Charu Goel Salma Kuhlmann Bruce Reznick
+ PDF Chat	Some new canonical forms for polynomials	2013	Bruce Reznick
+ PDF Chat	Congruence Properties of Binary Partition Functions	2013	Katherine Alexander Anders Melissa Dennison Jennifer Lansing Bruce Reznick
+	On the Length of Binary Forms	2013	Bruce Reznick
+	Pólya’s Theorem with zeros	2011	Mari Castle Victoria Powers Bruce Reznick
+ PDF Chat	ON THE SUMS OF TWO CUBES	2011	Bruce Reznick Jeremy Rouse
+	Congruence properties of binary partition functions	2011	Katherine Alexander Anders Melissa Dennison Bruce Reznick Jennifer L. Weber
+	Blenders	2011	Bruce Reznick
+	Congruence properties of binary partition functions	2011	Katherine L. Anders Melissa Dennison Bruce Reznick Jennifer L. Weber
+	On the length of binary forms	2010	Bruce Reznick
+	Laws of inertia in higher degree binary forms	2009	Bruce Reznick
+	A quantitative Pólya’s Theorem with zeros	2009	Mari Castle Victoria Powers Bruce Reznick
+	Laws of inertia in higher degree binary forms	2009	Bruce Reznick
+ PDF Chat	Let Me Tell You My Favorite Lattice-point Problem. . .	2008	Matthias Beck Benjamin Nill Bruce Reznick Carla D. Savage Ivan Soprunov Zhiqiang Xu
+	Let me tell you my favorite lattice-point problem …	2008	Matthias Beck Benjamin Nill Bruce Reznick Carla D. Savage Ivan Soprunov Zhiqiang Xu
+	On Hilbert's construction of positive polynomials	2007	Bruce Reznick
+	Regularity properties of the Stern enumeration of the rationals	2006	Bruce Reznick
+ PDF Chat	Almost Alternating Sums	2006	Kevin O’Bryant Bruce Reznick Monika Serbinowska
+	Almost Alternating Sums	2006	Kevin O’Bryant Bruce Reznick Monika Serbinowska
+	A quantitative Pólya's Theorem with corner zeros	2006	Victoria Powers Bruce Reznick
+	Clean Lattice Tetrahedra	2006	Bruce Reznick
+	Regularity properties of the Stern enumeration of the rationals	2006	Bruce Reznick
+	Polynomials Positive on Unbounded Rectangles	2005	Victoria Powers Bruce Reznick
+	On the absence of uniform denominators in Hilbert’s 17th problem	2005	Bruce Reznick
+	Integer Points in Polyhedra — Geometry, Number Theory, Algebra, Optimization	2005	Alexander Barvinok Mattias Beck Christian Haase Bruce Reznick Volkmar Welker
+ PDF Chat	Problems from the Cottonwood Room	2005	Matthias Beck Beifang Chen Lenny Fukshansky Christian Haase Allen Knutson Bruce Reznick Sinai Robins Annette Schürmann
+	Integer points in polyhedra - geometry, number theory, algebra, optimization : Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held in Snowbird, UT, July 13 - 17, 2003	2005	Matthias Beck Alexander Barvinok Christian Haase Bruce Reznick Volkmar Welker
+	Bounding the volume of facet-empty lattice tetrahedra	2005	Julián Pfeifle Han Duong Christian Haase Bruce Reznick
+ PDF Chat	A new approach to Hilbert's theorem on ternary quartics	2004	Victoria Powers Bruce Reznick Claus Scheiderer Frank Sottile
+	A New Proof of Hilbert's Theorem on Ternary Quartics	2004	Victoria Powers Bruce Reznick Claus Scheiderer Frank Sottile
+ PDF Chat	Positive Rational Solutions to x y = y mx : A Number-Theoretic Excursion	2004	Michael A. Bennett Bruce Reznick
+	A New Proof of Hilbert's Theorem on Ternary Quartics	2004	Victoria Powers Bruce Reznick Claus Scheiderer Frank Sottile
+ PDF Chat	Patterns of dependence among powers of polynomials	2003	Bruce Reznick
+	On the absence of uniform denominators in Hilbert's 17th problem	2003	Bruce Reznick
+	Almost Alternating Sums	2003	Kevin O’Bryant Bruce Reznick Monika Serbinowska
+	Nondivisibility of Binomial Coefficients: 10842	2002	Bruce Reznick GCHQ Problems Group Li Zhou
+ PDF Chat	Lattice Polytopes with Distinct Pair-Sums	2002	M. D. Choi T. Y. Lam Bruce Reznick
+	Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion	2002	Michael A. Bennett Bruce Reznick
+	Completely Multiplicative Functions: 10760	2001	Bruce Reznick Bruce Dearden
+	A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra	2001	Victoria Powers Bruce Reznick
+	Patterns of dependence among powers of polynomials	2001	Bruce Reznick
+	Polynomials that are positive on an interval	2000	Victoria Powers Bruce Reznick
+	Some concrete aspects of Hilbert’s 17th Problem	2000	Bruce Reznick
+	Notes towards a constructive proof of Hilbert’s theorem on ternary quartics	2000	Victoria Powers Bruce Reznick
+	Lattice polytopes with distinct pair-sums	2000	M. D. Choi T. Y. Lam Bruce Reznick
+	On the Nonmonotonicity of (\|Im(zn)\|)	1999	Bruce Reznick
+	None	1998	Zoltán Füredi Bruce Reznick
+	Homogeneous Polynomial Solutions to Constant Coefficient PDE's	1996	Bruce Reznick
+	Sums of 2m-th powers of rational functions in one variable over real closed fields	1996	M. D. Choi T. Y. Lam A. Prestel Bruce Reznick
+	Homogeneous Polynomial Solutions to Constant	1996	Bruce Reznick
+	Sums of 2m-th powers of rational functions in one variable over real closed fields	1996	M. D. Choi T. Y. Lam A. Prestel Bruce Reznick
+	Uniform denominators in Hilbert's seventeenth problem	1995	Bruce Reznick
+	Some constructions of spherical 5-designs	1995	Bruce Reznick
+ PDF Chat	An Inequality for Products of Polynomials	1993	Bruce Reznick
+ PDF Chat	An inequality for products of polynomials	1993	Bruce Reznick
+	Sums of even powers of real linear forms	1992	Bruce Reznick
+	Positive sextics and Schur's inequalities	1991	M. D. Choi T. Y. Lam Bruce Reznick
+	Some Binary Partition Functions	1990	Bruce Reznick
+	The sum of the squares of the parts of a partition, and some related questions	1989	Bruce Reznick
+	Forms derived from the arithmetic-geometric inequality	1989	Bruce Reznick
+ PDF Chat	Eigensharp Graphs: Decomposition into Complete Bipartite Subgraphs	1988	Thomas M. Kratzke Bruce Reznick Douglas B. West
+	Hooray for Calculus	1988	Bruce Reznick Bob McEliece Hal Fredricksen
+	Even symmetric sextics	1987	M. D. Choi T. Y. Lam Bruce Reznick
+	A quantitative version of Hurwitz' theorem on the arithmetic-geometric inequality.	1987	Bruce Reznick
+ PDF Chat	The asymptotic behavior of a family of sequences	1987	Paul Erdős Adolf Hildebrand Andrew Odlyzko Paul Pudaite Bruce Reznick
+	Lattice point simplices	1986	Bruce Reznick
+	Decomposition of product graphs into complete bipartite subgraphs	1985	Bruce Reznick Prasoon Tiwari Douglas B. West
+ PDF Chat	Some extremal problems for continued fractions	1985	Bruce Reznick
+	Continued fractions and an annelidic PDE	1983	Bruce Reznick
+	On Elementary Methods in Positivity Theory	1983	J. Gillis Bruce Reznick Doron Zeilberger
+ PDF Chat	Some inequalities for products of power sums	1983	Bruce Reznick
+ PDF Chat	Skewness in Banach Spaces	1983	Simon Fitzpatrick Bruce Reznick
+ PDF Chat	Skewness in Banach spaces	1983	Simon Fitzpatrick Bruce Reznick
+	The Pythagoras number of some affine algebras and local algebras.	1982	M. D. Choi Zhehao Dai T. Y. Lam Bruce Reznick
+ PDF Chat	Transversal zeros and positive semidefinite forms	1982	Man-Duen Choi Manfred Knebusch T. Y. Lam Bruce Reznick
+	Sums of squares in some integral domains	1980	M. D. Choi T. Y. Lam Bruce Reznick Alex Rosenberg
+	Real zeros of positive semidefinite forms. I	1980	Man Duen Choi Tsit Yuen Lam Bruce Reznick
+ PDF Chat	When is the iterate of a formal power series odd?	1979	Bruce Reznick
+ PDF Chat	Banach spaces with polynomial norms	1979	Bruce Reznick
+	Extremal PSD forms with few terms	1978	Bruce Reznick
+ PDF Chat	Banach spaces which satisfy linear identities	1978	Bruce Reznick
+ PDF Chat	A uniqueness criterion for fractional iteration	1974	Bruce Reznick

Common Coauthors

Coauthor	Papers Together
Victoria Powers	12
M. D. Choi	8
T. Y. Lam	8
Matthias Beck	5
Charu Goel	5
Salma Kuhlmann	5
Christian Haase	4
Jayadev S. Athreya	3
Jeremy T. Tyson	3
Kevin O’Bryant	3
Laura Felicia Matusevich	3
Frank Sottile	3
Monika Serbinowska	3
Melissa Dennison	3
Neriman Tokcan	3
Claus Scheiderer	3
Alessandro Oneto	2
Simon Fitzpatrick	2
Alexander Barvinok	2
Benjamin Nill	2
Douglas B. West	2
Jennifer L. Weber	2
Zhiqiang Xu	2
Ivan Soprunov	2
Boris Shapiro	2
Katherine Alexander Anders	2
Volkmar Welker	2
Carla D. Savage	2
Samuel Lundqvist	2
Mari Castle	2
A. Prestel	2
Paul Erdös	1
Prasoon Tiwari	1
Katherine L. Anders	1
Alex Rosenberg	1
Tsit Yuen Lam	1
Man Duen Choi	1
Man-Duen Choi	1
Charu Goel	1
Michael A. Bennett	1
Bruce Dearden	1
T. Y. Lam	1
Simone Sisneros-Thiry	1
GCHQ Problems Group	1
Katie Anders	1
Han Duong	1
Michael A. Bennett	1
Madeline Locus Dawsey	1
Zhehao Dai	1
Zoltán Füredi	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Sums of even powers of real linear forms	1992	Bruce Reznick	18
+	Über die Darstellung definiter Formen als Summe von Formenquadraten	1933	David Hilbert	18
+ PDF Chat	Ueber die Darstellung definiter Formen als Summe von Formenquadraten	1888	David Hilbert	14
+	Extremal positive semidefinite forms	1977	Man-Duen Choi T. Y. Lam	11
+	Ueber die Darstellung definiter Formen als Summen von Formenquadraten	1888	Hilbert	9
+	Some concrete aspects of Hilbert’s 17th Problem	2000	Bruce Reznick	9
+	History of the Theory of Numbers	1919	L. E. Dickson	9
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	8
+	Extremal PSD forms with few terms	1978	Bruce Reznick	8
+	Notes towards a constructive proof of Hilbert’s theorem on ternary quartics	2000	Victoria Powers Bruce Reznick	8
+ PDF Chat	The invariant theory of binary forms	1984	Joseph P. S. Kung Gian‐Carlo Rota	7
+	A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra	2001	Victoria Powers Bruce Reznick	7
+ PDF Chat	Lectures on Fermat's Last Theorem	1981	Lawrence C. Washington Paulo Ribenboim	6
+	LX. <i>On a remarkable discovery in the theory of canonical forms and of hyperdeterminants</i>	1851	J.J. Sylvester	6
+	Forms derived from the arithmetic-geometric inequality	1989	Bruce Reznick	6
+ PDF Chat	Lattice vertex polytopes with interior lattice points	1983	Douglas Hensley	5
+	Products of polynomials in many variables	1990	Bernard Beauzamy Enrico Bombieri Per Enflo Hugh L. Montgomery	5
+	Even symmetric sextics	1987	M. D. Choi T. Y. Lam Bruce Reznick	5
+	An Example of a Positive Polynomial which is not a Sum of Squares of Polynomials A Positive, but not Strongly Positive Functional	1979	Konrad Schmüdgen	5
+	On Stern's Diatomic Series	1929	D. H. Lehmer	5
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	5
+	Sums of squares of regular functions on real algebraic varieties	1999	Claus Scheiderer	5
+	Canonical forms for binary forms of even degree	1987	Joseph P. S. Kung	5
+	Real Even Symmetric Ternary Forms	1999	William R. Harris	5
+	On the Volume of Lattice Polyhedra	1957	J. E. Reeve	5
+	Sums of Squares of Polynomials	2000	Walter Rudin	5
+	Gundelfinger's Theorem on Binary Forms	1986	Joseph P. S. Kung	5
+	Uniform denominators in Hilbert's seventeenth problem	1995	Bruce Reznick	5
+	Groups and Geometric Analysis	2000	Sigurđur Helgason	4
+	On the Length of Binary Forms	2013	Bruce Reznick	4
+	Real zeros of positive semidefinite forms. I	1980	Man Duen Choi Tsit Yuen Lam Bruce Reznick	4
+	Extension of Hilbert's 1888 Theorem to Even Symmetric Forms	2014	Charu Goel	4
+	Waring's problem for the ring of polynomials	1979	Donald J. Newman M Slater	4
+	13 Lectures on Fermat’s Last Theorem	1979	Paulo Ribenboim	4
+ PDF Chat	An Introduction To The Theory Of Numbers	2008	G. H. Hardy E. M. Wright	4
+	Introduction to Fourier Analysis on Euclidean Spaces.	1971	Elias M. Stein Guido Weiss	4
+	Homogeneous Polynomial Solutions to Constant Coefficient PDE's	1996	Bruce Reznick	4
+ PDF Chat	Representing polynomials by positive linear functions on compact convex polyhedra	1988	David Handelman	4
+	The real holomorphy ring and sums of 2n-th powers	1982	Eberhard Becker	4
+	Lattice point simplices	1986	Bruce Reznick	4
+ PDF Chat	Power Sums, Gorenstein Algebras, and Determinantal Loci	1999	Anthony Iarrobino Vassil Kanev	4
+ PDF Chat	An Inequality for Products of Polynomials	1993	Bruce Reznick	3
+ PDF Chat	An algorithmic approach to Schmüdgen's Positivstellensatz	2002	Markus Schweighofer	3
+	The William Lowell Putnam mathematical competition: problems and solutions: 1965-1984	1985	Gerald L. Alexanderson Leonard F. Klosinski Loren C. Larson	3
+	A ‘Waring's problem’ for homogeneous forms	1969	W. J. Ellison	3
+ PDF Chat	On the typical rank of real binary forms	2011	Pierre Comon Giorgio Ottaviani	3
+ PDF Chat	Banach spaces which satisfy linear identities	1978	Bruce Reznick	3
+	An effective version of Pólya's theorem on positive definite forms	1996	Jesús A. De Loera Francisco Santos	3
+	On the positivity of symmetric polynomial functions.	2003	Vlad Timofte	3
+ PDF Chat	Approximation of the Stability Number of a Graph via Copositive Programming	2002	Etienne de Klerk Dmitrii V. Ṗasechnik	3