Peter Borwein

Q: What Schools Are Affiliated With Peter Borwein

Peter Borwein is affiliated with the following schools: University of Western Ontario, Simon Fraser University, University of Oxford, University of British Columbia, Dalhousie University

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Peter Borwein

Mathematics

#559

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#1070

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Measure Theory

#1067

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#1372

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Mathematics

Peter Borwein's Degrees

PhD Mathematics University of British Columbia

Why Is Peter Borwein Influential?

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According to Wikipedia, Peter Benjamin Borwein was a Canadian mathematician and a professor at Simon Fraser University. He is known as a co-author of the paper which presented the Bailey–Borwein–Plouffe algorithm for computing π.

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Peter Borwein'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

Polynomials and Polynomial Inequalities (1995) (925)
Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (1998) (657)
Pi and the AGM (1999) (564)
Modular Equations and Approximations to π (2000) (471)
On the rapid computation of various polylogarithmic constants (1997) (365)
A cubic counterpart of Jacobi’s identity and the AGM (1991) (254)
Computational Excursions in Analysis and Number Theory (2002) (201)
The Riemann Hypothesis (2008) (196)
Some cubic modular identities of Ramanujan (1994) (169)
The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (2010) (148)
Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi (1989) (136)
A complete description of Golay pairs for lengths up to 100 (2003) (111)
Müntz systems and orthogonal Müntz-Legendre polynomials (1994) (106)
The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) (100)
Littlewood‐Type Problems on [0,1] (1999) (78)
Polyphase sequences with low autocorrelation (2005) (76)
Generalizations of Müntz’s Theorem via a Remez-type inequality for Müntz spaces (1997) (70)
Pi: A Source Book (2004) (70)
Chebyshev polynomials: From approximation theory to algebra and number theory (1991) (66)
Binary sequences with merit factor greater than 6.34 (2004) (65)
On the irrationality of certain series (1992) (62)
Sharp extensions of Bernstein's inequality to rational spaces (1996) (60)
Multiple Roots of [−1, 1] Power Series (1998) (60)
Fuzzy cognitive maps and cellular automata: An evolutionary approach for social systems modelling (2012) (60)
On the zeros of polynomials with restricted coefficients (1997) (59)
Lehmer's problem for polynomials with odd coefficients (2007) (59)
Giuga's Conjecture on Primality (1996) (58)
Class number three Ramanujan type series for 1/p (1993) (55)
Making Sense of Experimental Mathematics (1996) (55)
On the complexity of familiar functions and numbers (1988) (54)
An efficient algorithm for the Riemann zeta function (1995) (53)
Visible Structures in Number Theory (2001) (49)
The integer Chebyshev problem (1996) (47)
Sign changes in sums of the Liouville function (2008) (45)
CHEBYSHEV POLYNOMIALS AND MARKOV-BERNSTEIN TYPE INEQUALITIES FOR RATIONAL SPACES (1994) (45)
Pi, Euler numbers, and asymptotic expansions (1989) (44)
Inequalities for compound mean iterations with logarithmic asymptotes (1993) (43)
On the irrationality of Σ (1/(qn+r)) (1991) (43)
The Full Müntz Theorem in C[0, 1] and L1[0, 1] (1996) (42)
On the Complexity of Calculating Factorials (1985) (40)
Ramanujan and Pi (1988) (38)
Classical and New Inequalities in Analysis, Mathematics and Its Applications (East European Series) Vol. 61, D. S. Mitrinovic J. E. Pecaric and A. M. Fink, Kluwer Academic, 1993, xvii + 740 pp. (1994) (38)
Strange series and high precision fraud (1992) (37)
LITTLEWOOD-TYPE PROBLEMS ON SUBARCS OF THE UNIT CIRCLE (1997) (37)
Polynomials with coefficients from a finite set (2008) (37)
Scientific computation on mathematical problems and conjectures (1991) (36)
The Prouhet—Tarry—Escott Problem (2002) (36)
THE EXPECTED Lp NORM OF RANDOM POLYNOMIALS (2001) (36)
Affine Weyl groups (2001) (34)
On the Generating Function of the Integer Part: [nα + γ] (1993) (33)
Quadratic Hermite-Padé approximation to the exponential function (1986) (33)
Explicit merit factor formulae for Fekete and Turyn polynomials (2001) (31)
Some computations on the spectra of Pisot and Salem numbers (2002) (31)
Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point (1997) (29)
A sharp Bernstein-type inequality for exponential sums. (1995) (29)
The Arc Length of the Lemniscate { | p(z) | = 1} (1995) (28)
The Littlewood Problem (2002) (28)
On the zeros of cosine polynomials: solution to a problem of Littlewood (2008) (27)
Rudin-Shapiro-like polynomials in L4 (2000) (27)
An old conjecture of Erdos-Turán on additive bases (2005) (27)
Stieltjes and other integral representations for functions of Lambert W (2012) (27)
Wieferich pairs and Barker sequences, II (2013) (26)
The Way of All Means (1987) (26)
A remarkable cubic mean iteration (1990) (26)
Completely multiplicative functions taking values in $\{-1,1\}$ (2008) (26)
Number Theory and Polynomials: Barker sequences and flat polynomials (2008) (25)
Location of Zeros (2002) (24)
Zeros of Chebyshev polynomials in Markov systems (1990) (23)
Zeros of Partial Sums of the Riemann Zeta Function (2007) (23)
Markov’s inequality for polynomials with real zeros (1985) (23)
Polynomials with Height 1 and Prescribed Vanishing at 1 (2000) (23)
The Mahler Measure of Polynomials with Odd Coefficients (2004) (23)
The social impact in a high-risk community: A cellular automata model (2011) (22)
The expected _{} norm of random polynomials (2000) (22)
Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros (1994) (22)
Müntz spaces and Remez inequalities (1995) (21)
Bivariate segment approximation and free knot splines: Research problems 96-4 (1996) (20)
Computational investigations of the Prouhet-Tarry-Escott Problem (2003) (20)
Power series with restricted coefficients and a root on a given ray (1998) (20)
The Erdős—Szekeres Problem (2002) (20)
Hypergeometric analogues of the arithmetic-geometric mean iteration (1993) (19)
Monic integer Chebyshev problem (2003) (19)
Transcendence of power series for some number theoretic functions (2008) (18)
TERRY SHEIL-SMALL: 428 pp., £65.00 (US$95.00), ISBN 0-521-40068-6 (Cambridge University Press, 2002) (2004) (18)
On Cyclotomic Polynomials with ± 1 Coefficients (1999) (17)
Lower bounds for the number of zeros of cosine polynomials in the period (2007) (17)
Exact Inequalities for the Norms of Factors of Polynomials (1994) (17)
The density of alternation points in rational approximation (1989) (17)
Merit Factors of Polynomials Formed by Jacobi Symbols (2001) (17)
Markov- and Bernstein-Type Inequalities for Polynomials with Restricted Coefficients (1997) (16)
An Interesting Infinite Product (1993) (16)
The _{} version of Newman’s Inequality for lacunary polynomials (1996) (15)
Ramanujan, modular equations and pi or how to compute a billion digits of pi (1989) (15)
Nikolskii-type inequalities for shift invariant function spaces (2006) (15)
Pointwise Remez- and Nikolskii-type inequalities for exponential sums (2000) (15)
Moment-Matching and Best Entropy Estimation (1994) (15)
Number Theory and Polynomials: The merit factor problem (2008) (14)
The multiplicity of the zero at 1 of polynomials with constrained coefficients (2013) (14)
Pad6 Approximants for the q-Elementary Functions (1988) (14)
Merit Factors of Character Polynomials (2000) (14)
Champernowne’s Number, Strong Normality, and the X Chromosome (2013) (14)
An extremal property of Fekete polynomials (2000) (14)
Computation of π by Successive Interpolations (1997) (14)
Rudin—Shapiro Polynomials (2002) (13)
Markov's and Bernstein's Inequalities on Disjoint Intervals (1981) (13)
Markov and Bernstein type Inequalities in Lp for Classes of Polynomials with Constraints (1995) (13)
Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros (1992) (13)
Explicit Ramanujan-type approximations to pi of high order (1987) (12)
The average norm of polynomials of fixed height (2006) (12)
Measurement of a Circle (2000) (12)
Using Varieties of Simulation Modeling for Criminal Justice System Analysis (2008) (12)
Newman's Inequality for Müntz Polynomials on Positive Intervals (1996) (12)
The relationship between the zeros of best approximations and differentiability (1984) (12)
Growth of the product $∏^n_{j=1} (1-x^{a_j})$ (1998) (11)
On Littlewood Polynomials with Prescribed Number of Zeros Inside the Unit Disk (2015) (11)
Upper bounds for the derivative of exponential sums (1995) (10)
Newman polynomials with prescribed vanishing and integer sets with distinct subset sums (2003) (10)
The Multivariate Integer Chebyshev Problem (2009) (9)
Challenges in mathematical computing (2001) (9)
General Forms for Minimal Spectral Values For a Class of Quadratic Pisot Numbers (2003) (9)
On Monochrome Lines and Hyperplanes (1982) (9)
On the Denseness of Weighted Incomplete Approximations (1992) (9)
Cubic and Higher Order Algorithms for π (1984) (9)
Markov-Bernstein type inequalities under Littlewood-type coefficient constraints☆ (2000) (9)
Some Restricted Partition Functions (1993) (9)
ON THE IRRATIONALITY OF A CERTAIN Q SERIES (1999) (8)
The Usual Behaviour of Rational Approximations (1983) (8)
Notes on lacunary Müntz polynomials (1991) (8)
A Dictionary of Real Numbers (1991) (8)
Gero-modelling: new ways of looking at 'old' issues (2012) (8)
Reduced complexity evaluation of hypergeometric functions (1987) (8)
Rational approximations with real poles to e−xand xn (1983) (8)
Trigonometric polynomials with many real zeros and a Littlewood-type problem (2000) (8)
The arc length of the lemniscate {\vert()\vert=1} (1995) (8)
Variations on Müntz's Theme (1991) (8)
Why This Book (2008) (8)
Sign Changes of the Liouville Function on Quadratics (2011) (7)
A Conjecture Related to Sylvester's Problem (1983) (7)
On the mean iteration (a,b) ← (a+3b/4, √ab+b/2) (1989) (7)
Mathematicians on Creativity (2014) (7)
Muntz's Theorem on compact subsets of positive measure (1995) (7)
Norms of cyclotomic Littlewood polynomials (2005) (7)
The size of {x: rn′rn ⩾ 1} and lower bounds for ∥e−x − rn∥ (1982) (7)
A very rapidly convergent product expansion for π (1983) (7)
Zeros of Iterated Integrals of Polynomials (1995) (6)
Explicit construction of general multivariate Padé approximants to an Appell function (2005) (6)
The Desmic Conjecture (1983) (6)
Dense Markov Spaces and Unbounded Bernstein Inequalities (1995) (6)
Rational approximation to Lipschitz and Zygmund classes (1992) (6)
Computational and Analytical Mathematics (2013) (6)
Irreducible polynomials and barker sequences (2007) (6)
Rational Approximation with Varying Weights (1997) (6)
More quadratically converging algorithms for p (1986) (6)
Lacunary Müntz systems (1993) (6)
Markov and Bernstein type inequalities on subsets of [−1,1] and [−π, π] (1994) (5)
Rational interpolation to ex (1982) (5)
Strange series evaluations and high precision fraud (1992) (5)
The usual behavior of rational approximation, II (1993) (5)
On approximation by trigonometric Lagrange interpolating polynomials (1989) (5)
Rational approximation with varying weights I (1996) (5)
Extremal Mahler measures and _{} norms of polynomials related to Barker sequences (2013) (5)
Sylvester’s problem and Motzkin’s theorem for countable and compact sets (1984) (5)
On the mean iteration (,)←((+3)/4,(√+)/2) (1989) (5)
Euclidean reflection groups (2001) (5)
A NOTE ON BARKER POLYNOMIALS (2012) (5)
Approximating $\pi$ with Ramanujan's solvable modular equations (1989) (5)
Experimental Mathematics: A Discussion (2001) (5)
Questions About Polynomials with ${0,-1,+1}$ Coefficients: Research Problems 96-3, Edited by P.Borwein, I.Daubechies, and V.Totik (1996) (4)
Expected Norms of Zero-One Polynomials (2008) (4)
Inequalities and Inverse Theorems in Restricted Rational Approximation Theory (1980) (4)
Non-trivial quadratic approximations to zero of a family of cubic Pisot numbers (2003) (4)
On a class of polynomials related to Barker sequences (2012) (4)
Generalizations of Gonçalves’ inequality (2005) (3)
On Padé and Best Rational Approximation (1983) (3)
Tools for visualizing real numbers : Planar number walks (2012) (3)
On Sylvester's problem and Haar spaces. (1983) (3)
Rational Interpolation to $e^x $, II (1985) (3)
On the mean iteration $ (a,b)\rightarrow((a+3b)/4,(\surd ab+b)/2)$ (1989) (3)
Uniform Approximation by Polynomials with Variable Exponents (1983) (3)
An Eecient Algorithm for the Riemann Zeta Function (1995) (3)
Approximations with negative roots and poles (1982) (3)
High-Level Simulation Model of a Criminal Justice System (2014) (3)
An explicit cubic iteration for π (1986) (3)
The Experts Speak for Themselves (2008) (2)
Some questions of Erdős and Graham on numbers of the form ∑_{}/2^{_{}} (1990) (2)
The Full M Untz Theorem in C0; 1] and L 1 0; 1] (1999) (2)
ON THE ZEROS OF COSINE POLYNOMIALS : SOLUTION TO AN OLD PROBLEM OF LITTLEWOOD (2)
SOME QUESTIONS OF ERDÖS AND GRAHAM ON NUMBERS OF THE FORM £ gJ 2 g " (2007) (2)
On the irrationality of a certain multivariate q series (2003) (2)
The Extraordinary Power of Division in Straight Line Programs (2012) (2)
Questions about polynomials with {0, −1, +1} coefficients: Research problems 96-3 (1996) (2)
Rational approximations to Stieltjes transforms. (1983) (2)
Hypergeometric analogues of the AGM iteration (1993) (2)
Lower bounds for the merit factors of trigonometric polynomials from Littlewood classes (2003) (2)
On Monochromatic Triangles (1984) (2)
Remote Collaboration (2012) (2)
The Easier Waring Problem (2002) (2)
Mathematical Circles: A Selection of Mathematical Stories and Anecdotes (2000) (2)
Explicit Algebraic Nth Order Approximations to PI (1984) (2)
A Remez-Type Inequality for Non-dense Müntz Spaces with Explicit Bound (1998) (2)
Some Special Polynomials (1995) (1)
Quadratically converging rational mean iterations (1991) (1)
Pi, Euler numbers and asymptotic expansions | NOVA. The University of Newcastle's Digital Repository (1989) (1)
Tools for visualizing real numbers . Part I : Planar number walks (2012) (1)
Approximations by rational functions with positive coefficients (1980) (1)
Some Computations on Pisot and Salem Numbers (2000) (1)
A Functional Equation (David W. Wilson) (1990) (1)
On a method of Newman and a theorem of Bernstein (1982) (1)
Rational functions with positive coefficients, polynomials and uniform approximations (1980) (1)
Barker Polynomials and Golay Pairs (2002) (1)
A VARIANT OF LIOUVILLE ’ S LAMBDA FUNCTION : SOME SURPRIZING FORMULAE (1)
Introduction and Basic Properties (1995) (1)
Approximation of xn by reciprocals of polynomials (1981) (1)
The density of rational functions in Markov systems: A counterexample to a conjecture of D. J. Newman (1993) (1)
MÜNTZ SYSTEMS AND MÜNTZ – LEGENDRE POLYNOMIALS (1999) (1)
Introduction: Reflection groups and invariant theory (2001) (1)
Mathematical Malaises: Pi In the Sky . Counting, Thinking, and Being. John D. Barrow. Clarendon (Oxford University Press), New York, 1992. xii, 317 pp., illus. $25. (1993) (1)
The Rhind Mathematical Papyrus-Problem 50 ( ~ 1650 B.C.) (1997) (1)
Transcendence of the Gaussian Liouville number and relatives (2008) (1)
Digitally Activated Mathematics for a Brave New World Wide Web (1996) (1)
Gregory. Correspondence with John Collins (1671) (2000) (0)
Diophantine Approximation of Zeros (2002) (0)
Eco. An excerpt from Foucault’s Pendulum (1993) (2000) (0)
EXPANSION FOR rc (1983) (0)
A Polynomial Problem (1980) (0)
Ramanujan and pi [redacted] (2001) (0)
Arbitrarily slow rational approximations on the positive real line (1978) (0)
Strong Normality of Numbers (0)
Eigenvalues for reflection groups (2001) (0)
Ring of invariants and eigenvalues (2001) (0)
Extensions of the Riemann Hypothesis (2008) (0)
Walking on real numbers (2013) (2016) (0)
Squaring the Circle (2000) (0)
The ring of invariants (2001) (0)
Failed Attempts at Proof (2008) (0)
THE Lp VERSION OF NEWMAN ' SINEQUALITY FOR LACUNARY POLYNOMIALSPeter (2007) (0)
On the genesis of BBP formulas (2021) (0)
Pisot and Salem Numbers (2002) (0)
The Impact of Social Interactions on the Spread of HIV Infection among Injection Drug Users : A Cellular Automaton Model (2010) (0)
Newton on line: The electronic revolution in mathematics (1997) (0)
Wallis. Arithmetica Infinitorum (1655) (2000) (0)
Huygens. De Circuli Magnitudine Inventa (1724) (2000) (0)
Walks on real numbers. (2012) (0)
Reflection groups and Coxeter systems (2001) (0)
Classification of Coxeter systems and reflection groups (2001) (0)
RATIONALINTERPOLATIONTO e x, II.* (1985) (0)
Mathematical malaises. (1993) (0)
The extended ring of invariants (2001) (0)
Modern Approaches in Asymptotics of Polynomials (2008) (0)
Walking on Real Numbers (2012) (0)
Elementary Problems: E3445-E3450 (1991) (0)
Ramanujan and pi (1988) (2016) (0)
The Classification of crystallographic root systems (2001) (0)
Book reviewChebyshev polynomials: From approximation theory to algebra and number theory: T. J. Rivlin, Wiley-Interscience, 1990, 249 pp (1991) (0)
Correspondence. Ludolph (or Ludolff or Lucius) van Ceulen (2004) (0)
AN EXTREMAL PROPERTY OF FEKETE POLYNOMIALSPETER BORWEIN (1999) (0)
6 IS MATHEMATICS INVADING HUMAN CELLS? IMPRESSIONS FROM A COLLABORATION WITH DIABETES DOCTORS / Bernhelm (2013) (0)
Pi, Euler numbers, and asymptotic expansions (1989) (2016) (0)
A NOTE ON BARKER POLYNOMIALS Peter Borwein and Tamás Erdélyi (2014) (0)
∼2.71828: e . The Story of a Number. Eli Maor. Princeton University Press, Princeton, NJ, 1994. xiv, 214 pp. $24.95 or £19.95. (1994) (0)
Newton.Of the Method of Fluxions and Infinite Series (1737) (2004) (0)
On the behavior of mle of the scale parameter of the student family (1984) (0)
Assuming the Riemann Hypothesis and Its Extensions (2008) (0)
D It B_,lIIV (0)
Properties of regular elements (2001) (0)
A singular genius. (1991) (0)
Hypertranscendence of the functional equation ( (1989) (0)
Products of Cyclotomic Polynomials (2002) (0)
Lambert. Irrationality of π (2000) (0)
Erratum to “On the irrationality of a certain multivariate series” (2004) (0)
Extract from the Rhind Papyrus (2004) (0)
Inequalities in Müntz Spaces (1995) (0)
Chebyshev and Descartes Systems (1995) (0)
69.30 A remarkable approximation to π (2004) (0)
Restricted uniform rational approximations (1979) (0)
On the Mean Iteration ( a , b ) + ( a + 3 b x ? + b ) (2007) (0)
Inequalities for Rational Function Spaces (1995) (0)
The Banū Mūsā: The Measurement of Plane and Solid Figures ( ~ 850) (2000) (0)
Advanced Problems: 6126-6131 (1977) (0)
A convergence problem for rational interpolants with preassigned poles: Research problem 96-1 (1996) (0)
The Deconstruction of Pi (2004) (0)
Corrigendum: The density of rational functions in markov systems: a counterexample to a conjecture of D. J. Newman (1995) (0)
Polynomials whose reducibility is related to the Goldbach conjecture (2014) (0)
On the mean iteration $(a,b)\leftarrow ((a+3b)/4,(\sqrt{ab}+b)/2)$ (1989) (0)
The Life of π (2014) (2016) (0)
Bilinear forms of Coxeter systems (2001) (0)
Representations of pseudo-reflection groups (2001) (0)
Algorithms for Calculating ζ(s) (2008) (0)
A Pamphlet on Pi serving as a Supplement for the Third Edition of Pi : A Source Book (2003) (0)
Wallis. Computation of π by Successive Interpolations (2004) (0)
Poincaré series for the ring of covariants (2001) (0)
ORTHOGONALITY AND IRRATIONALITY (1994) (0)
Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (2000) (0)
The Resolution of Some Conjectures via a Remez-Type Inequality for Muntz Spaces (1993) (0)
[V.] The Ratio of the Diameter of any Circle to its Circumference is One [That is, is The Same for All Circles]. (2004) (0)
Matrix transformations of series of orthogonal polynomials (1995) (0)
Wallis. Computation of π by Successive Interpolations (1655) (2000) (0)
My Brian Is Open (Book Review). (2000) (0)
A Pamphlet on Pi (2003) (0)
Eigenvalues for regular elements (2001) (0)
LOWER BOUNDS FOR NORMS OF PRODUCTS OF POLYNOMIALS VIA BOMBIERI INEQUALITY (2012) (0)
Ramanujan et Pi (1988) (0)
Scientific Notes a N E X P L I C I T C U B I C I T E R a T I O N F O R N (0)
Scientific Notes a Very Rapidly Convergent Product Expansion for Rc (2005) (0)
Classifications of pseudo-reflection groups (2001) (0)
A workshop on Computational and Analytical Mathematics in honour of Jonathan Borwein ’ s 60 th Birthday May 16 – 20 , 2011 Report prepared (0)
N-th digit computation (2003) (0)
LLL and PSLQ (2002) (0)
Inequalities for compound means with logarithmic asymptotes (1993) (0)
Of the Method of Fluxions and Infinite Series (1737) (1997) (0)
On the Use of the Discovered Factors to Sum Infinite Series (2000) (0)
Harmonics and reflection groups (2001) (0)
Roots of $\{0,+1,-1\}$ Polynomials. (1996) (0)
Nonmodular invariants of pseudo-reflection groups (2001) (0)

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