Bruce Reznick | Academic Influence

Bruce Reznick's AcademicInfluence.com Rankings

Bruce Reznick

Mathematics

#1138

World Rank

#1919

Historical Rank

#488

USA Rank

Measure Theory

#3268

World Rank

#3863

Historical Rank

#946

USA Rank

mathematics Degrees

Download Badge

Mathematics

Bruce Reznick's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Bruce Reznick Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Bruce Reznick is an American mathematician long on the faculty at the University of Illinois at Urbana–Champaign. He is a prolific researcher noted for his contributions to number theory and the combinatorial-algebraic-analytic investigations of polynomials. In July 2019, to mark his 66th birthday, a day long symposium "Bruce Reznick 66 fest: A mensch of Combinatorial-Algebraic Mathematics" was held at the University of Bern, Switzerland.

(See a Problem?)

Bruce Reznick's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Sums of squares of real polynomials (1995) (387)
Sums of Even Powers of Real Linear Forms (1992) (228)
Some concrete aspects of Hilbert's 17th Problem (2000) (202)
A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra (2001) (198)
Extremal PSD forms with few terms (1978) (172)
Uniform denominators in Hilbert's seventeenth problem (1995) (152)
Polynomials that are positive on an interval (2000) (115)
Real zeros of positive semidefinite forms. I (1980) (87)
Some Binary Partition Functions (1990) (75)
Forms derived from the arithmetic-geometric inequality (1989) (71)
Even symmetric sextics (1987) (69)
On Hilbert's construction of positive polynomials (2007) (59)
Eigensharp graphs: decomposition into complete bipartite subgraphs (1988) (46)
On Elementary Methods in Positivity Theory (1983) (44)
ON THE LENGTH OF BINARY FORMS (2010) (39)
Lattice point simplices (1986) (38)
Sums of Squares in Some Integral Domains (1980) (38)
Notes towards a constructive proof of Hilbert's theorem on ternary quartics (2000) (37)
Regularity Properties of the Stern Enumeration of the Rationals (2006) (34)
On the absence of uniform denominators in Hilbert's 17th problem (2003) (33)
Homogeneous Polynomial Solutions to Constant Coefficient PDE's (1996) (32)
Some constructions of spherical 5-designs☆ (1995) (30)
A new approach to Hilbert's theorem on ternary quartics (2004) (30)
Cantor Set Arithmetic (2017) (26)
An inequality for products of polynomials (1993) (25)
A quantitative version of Hurwitz' theorem on the arithmetic-geometric inequality. (1987) (23)
Clean Lattice Tetrahedra (2006) (19)
Polynomials positive on unbounded rectangles (2005) (18)
Problems from the Cottonwood room (2005) (17)
Banach spaces with polynomial norms (1979) (17)
A quantitative Pólya's Theorem with corner zeros (2006) (16)
Transversal zeros and positive semidefinite forms (1982) (15)
A Turán Inequality Arising in Information Theory (1981) (14)
The asymptotic behavior of a family of sequences (1987) (14)
Decomposition of product graphs into complete bipartite subgraphs (1985) (13)
On the sums of two cubes (2010) (13)
SOME NEW CANONICAL FORMS FOR POLYNOMIALS (2012) (13)
A quantitative Pólya's Theorem with zeros (2009) (13)
On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms (2015) (13)
Lattice Polytopes with Distinct Pair-Sums (2000) (13)
The analogue of Hilbert's 1888 theorem for Even Symmetric Forms (2015) (13)
On generic and maximal k-ranks of binary forms (2017) (12)
LAWS OF INERTIA IN HIGHER DEGREE BINARY FORMS (2009) (11)
Almost Alternating Sums (2003) (11)
Banach spaces which satisfy linear identities (1976) (10)
Pólya's Theorem with zeros (2011) (9)
Let Me Tell You My Favorite Lattice-point Problem. . . (2007) (8)
Sums of 2m-th powers of rational functions in one variable over real closed fields (1996) (8)
Patterns of Dependence Among Powers of Polynomials (2001) (8)
Congruence Properties of Binary Partition Functions (2011) (8)
Some inequalities for products of power sums (1983) (8)
Positive sextics and Schur's inequalities (1991) (8)
When is the iterate of a formal power series odd? (1979) (7)
Binary forms with three different relative ranks (2016) (7)
A note on mediated simplices (2019) (7)
Skewness in Banach spaces (1983) (4)
The Non-Tightness of a Convex Relaxation to Rotation Recovery (2021) (4)
The sum of the squares of the parts of a partition, and some related questions (1989) (4)
Some extremal problems for continued fractions (1985) (3)
Digital representations using the greatest integer function (1989) (3)
A New Proof of Hilbert's Theorem on Ternary Quartics (2004) (3)
Problems: 10620-10626 (1997) (2)
Positive Rational Solutions to xy = ymx: A Number-Theoretic Excursion (2004) (2)
A uniqueness criterion for fractional iteration (1974) (2)
Cantor's Singular Moments: 10621 (1999) (2)
Mathematical ENQUIRER (2007) (1)
Elementary Problems: E2434,E2462-E2467 (1974) (1)
Equal sums of two cubes of quadratic forms (2021) (1)
Elementary Problems: E2486-E2490 (1974) (1)
Continued fractions and an annelidic PDE (1983) (1)
Review: Donald J. Newman, A problem seminar (1984) (1)
Elementary Problems: E3054-E3058 (1984) (1)
The classification of 1-point lattice tetrahedra (1)
On the Nonmonotonicity of (|Im(zn)|) (1999) (1)
Sums of 2m-th powers of rational functions in one variable over real closed fields (1996) (1)
The Maximal Angular Gap among Rectangular Grid Points (1998) (0)
Creative Blocking Faculty Advisor : (2013) (0)
STERN NOTES , CHAPTER 8 ( FIRST DRAFT ) (0)
MATH 417 –SIXTH WEEK (2020) (0)
Lattice reformulation of integer programming problems (2008) (0)
Homogeneous Polynomial Solutions to Constant (1996) (0)
A Set is a Set (Sung to the tune of the theme to “Mr. Ed”) (1993) (0)
The American Mathematical Monthly (2018) (0)
Problem 10842 (2000) (0)
Sparse versions of the Cayley–Bacharach theorem (2019) (0)
STERN NOTES , CHAPTER 5 ( VERSION 1 ) (0)
Elementary Problems: E3207-E3212 (1987) (0)
Advanced Problems: 6392 (1982) (0)
TR-2005-006 A New Proof of Hilbert ’ s Theorem on Ternary Quartics by Victoria Powers (2007) (0)
Equal sums of two cubes of binary quadratic forms (2020) (0)
Linearly dependent powers of binary quadratic forms (2019) (0)
Elementary Problems: E3243-E3248 (1988) (0)
Polynomials Positive on Unbounded Rectangles Victoria Powers ? (2004) (0)
An Inequality for Products of Polynomials Author ( s ) : (1993) (0)
On the analogue of Hilbert's 1888 Theorem for Symmetric and Even Symmetric Forms (2015) (0)
TR-2005-005 Polynomials Positive on Unbounded Rectangles by Victoria Powers (2007) (0)
Elementary Problems: E3469-E3474 (1991) (0)
Bounding the volume of facet-empty lattice tetrahedra (2005) (0)
Contemporary Mathematics Problems from the Cottonwood Room (2013) (0)
Polynomials That Are Positive on an IntervalVictoria PowersEmory University (2006) (0)
Elementary Problems: E3046-E3047 (1984) (0)
One Introduction to Mathematical Research (2006) (0)
STERN NOTES , MATH 595 , SPRING 2012 (0)
Elementary Problems: E3219-E3224 (1987) (0)
Problems and Solutions: Elementary Problems: E2480-E2485 (1974) (0)
Nondivisibility of Binomial Coefficients: 10842 (2002) (0)
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) (0)
Congruence Properties of Binary Partition Functions (2013) (0)
Hooray for Calculus (1988) (0)
MATH 417 – SECOND WEEK (2020) (0)
Completely Multiplicative Functions: 10760 (2001) (0)
Elementary Problems: E2731-E2736 (1978) (0)
MATH 417 –FIFTH WEEK (2020) (0)
ON THE NON-MONOTONICITY OF (jIm(zn)j) (1998) (0)

This paper list is powered by the following services:

Other Resources About Bruce Reznick

en.wikipedia.org

What Schools Are Affiliated With Bruce Reznick?

Bruce Reznick is affiliated with the following schools: