# Peter Borwein

#9,132

Most Influential Person Now

Canadian mathematician

## Peter Borwein's AcademicInfluence.com Rankings

Peter Borweinmathematics Degrees

Mathematics

#559

World Rank

#1070

Historical Rank

Measure Theory

#1067

World Rank

#1372

Historical Rank

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Mathematics

## Peter Borwein's Degrees

- PhD Mathematics University of British Columbia

## Why Is Peter Borwein Influential?

(Suggest an Edit or Addition)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.

## Peter Borwein's Published Works

### 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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## What Schools Are Affiliated With Peter Borwein?

Peter Borwein is affiliated with the following schools: