Publications by Peter Borwein
Available at http://www.cecm.sfu.ca/~pborwein
Only recent papers are available online in pdf form.
For other papers or other formats please
contact me.
The online publications below are NOT necessarily authoritative nor
necessarily final versions. They are listed in reverse chronological order
of writing.
Books
2007 The Riemann Hypothesis: A resource for the afficionado and virtuoso alike
2004 Pi: a source book (MR2065455)
2002 Computational excursions in analysis and number theory (MR1912495)
2000 Pi: a source book (MR1746004)
1998 Pi and the AGM. A study in analytic number theory and computational complexity (MR1641658)
1995 Polynomials and polynomial inequalities (MR1367960)
1990 A dictionary of real numbers (MR1030542)
1987 Pi and the AGM. A study in analytic number theory and computational complexity. (MR0877728)
Papers
Other Manuscripts
 Goldbach
Polynomials
 Transcendance of the Gaussian Liouville number and relatives
 Strong normality of numbers
 A variant of Liouville's lambda function: some surprising formulae
 Reverse symbolic computations, the identity function
 Challenges in mathematical computing
 The amazing number Pi
 Othogonality and irrationality
 Some observations on computer aided analysis
2011

Champernowne and Normality
2010

Completely Multiplicative Functions
2009
 The
Multivariate Integer Chebyshev Problem
 Transcendence
of some power series
2008
 On the zeros of cosine polynomials: solution to a problem of Littlewood
 Polynomials with coefficients from a finite set
 Sign changes in the sums of the Liouville function (MR2398787)
 Expected norms of 01 polynomials
 The merit factor problem
 Barker sequences and flat polynomials
2007
 Lower bounds for the number of zeros of cosine polynomials in the period: a problem of Littlewood (MR2320719)
 Irreducible polynomials and Barker sequences (MR2404490)
 Generalizations of Gonçalves' inequality (MR2280202)
 Lehmer's problem for polynomials with odd coefficients (MR2373144)
 Zeros of partial sums of the Riemann zeta function (MR2312975)
 The average norm of polynomials of fixed height (MR2255202)
2006
 Nikolskiitype inequalities for shift invariant function spaces (MR2231907)
 An old conjecture of ErdösTuràn on additive bases (MR2176410)
2005
 Norms of cyclotomic Littlewood polynomials (MR2132173)
 Polyphase sequences with low autocorrelation (MR2241514)
 Explicit construction of general multivariate Padé approximants to an Appell function (MR2127575)
2004
 The Mahler measure of polynomials with odd coefficients (MR2038720)
 Binary sequences with merit factor greater than 6.34 (MR2103494)
 A complete description of Golay pairs for lengths up to 100 (MR2031419)
2003
 Newman polynomials with prescribed vanishing and integer sets with distinct subset sums (MR1954968)
 Lower bounds for the merit factors of trigonometric polynomials from Littlewood classes (MR2019608)
 Monic integer Chebyshev problem (MR1986811)
 Nontrivial quadratic approximations to zero of a family of cubic Pisot numbers (MR1997583)
 General forms for minimal spectral values for a class of quadratic Pisot numbers (MR1934431)
 Computational investigations of the ProuhetTarryEscott problem (MR1986822)
 On the irrationality of a certain multivariate q series (MR1963741)
 Erratum to: "On the irrationality of a certain multivariate q series" (MR2063136)
2002
 Paul Erdös and polynomials (MR1954691)
 Some computations on the spectra of Pisot and Salem numbers (MR1885627)
 Explicit merit factor formulae for Fekete and Turyn polynomials (MR1859033)
2001
 An extremal property of Fekete polynomials (MR1784013)
 Merit factors of polynomials formed by Jacobi symbols (MR1814964)
 Ramanujan and π (MR1862751)
 The expected L_{p} norm of random polynomials (MR1814174)
 Trigonometric polynomials with many real zeros and a Littlewoodtype problem (MR1801998)
 Visible structures in number theory (MR1954492)
2000
 An efficient algorithm for the Riemann zeta function (MR1777614)
 Polynomials with height 1 and prescribed vanishing at 1 (MR1795875)
 Pointwise Remez and Nikolskiitype inequalities for exponential sums (MR1735078)
 Merit factors of character polynomials (MR1766099)
 RudinShapirolike polynomials in L_{4} (MR1709147)
 MarkovBernstein type inequalities under Littlewoodtype coefficient constraints (MR1813157)
1999
 On cyclotomic polynomials with ±1 coefficients (MR1737235)
 On the irrationality of a certain q$ series (MR1485462)
 Littlewoodtype problems on [0,1] (MR1687555)
1998
 On the irrationality of ∑_{{i=0}}^{∞}q^{i}∏_{{j=0}}^{i}(1+q^{j}r+q^{2j}s) (MR1742990)
 Some old problems on polynomials with integer coefficients (MR1742989)
 Growth of the product ∏_{j=1}^{n}(1x^{aj}) (MR1654470)
 Power series with restricted coefficients and a root on a given ray (MR1468939)
 Multiple roots of [1,1] power series (MR1624809)
 Muntz's theorem on compact subsets of positive measure (MR1625223)
 Remeztype inequality for nondense Müntz spaces with explicit bound (MR1624834)
1997
 What is organic mathematics? (MR1483911)
 Littlewoodtype problems on subarcs of the unit circle (MR1631600)
 On the zeros of polynomials with restricted coefficients (MR1468873)
 The quest for pi (MR1439159)
 Polynomials with {0,+1,1} coefficients and a root close to a given point (MR1604114)
 Markov and Bernsteintype inequalities for polynomials with restricted coefficients (MR1606930)
 On the rapid computation of various polylogarithmic constants (MR1415794)
 Generalizations of Müntz's theorem via a Remeztype inequality for Müntz spaces (MR1415318)
 Sharp extensions of Bernstein's inequality to rational spaces (MR1433285)
 Ramanujan, modular equations, and approximations to pi or How to compute one billion digits of pi (MR1483913)
1996
 Questions about polynomials with {0,1,+1} coefficients: Research Problems 963 (MR1405009)
 Making sense of experimental mathematics (MR1413248)
 A sharp Bernsteintype inequality for exponential sums (MR1401698)
 Newman's inequality for Müntz polynomials on positive intervals (MR1385812)
 The L_{p} version of Newman's inequality for lacunary polynomials (MR1285974)
 Giuga's conjecture on primality (MR1369150)
 The full Müntz theorem in C[0,1] and L_{1}[0,1] (MR1395070)
 Rational approximation with varying weights. I (MR1393288)
 The integer Chebyshev problem (MR1333305)
1995
 Matrix transformations of series of orthogonal polynomials (MR1376739)
 Müntz spaces and Remez inequalities (MR1273395)
 The arc length of the lemniscate { p(z) =1} (MR1223265)
 Incomplete rational approximation in the complex plane (MR1323965)
 Zeros of iterated integrals of polynomials (MR1319690)
 Dense Markov spaces and unbounded Bernstein inequalities (MR1323752)
 Upper bounds for the derivative of exponential sums (MR1232137)
 Corrigendum: "The density of rational functions in Markov systems: a counterexample to a conjecture of D. J. Newman" (MR1323967)
 Markov and Bernstein type inequalities in L_{p} for classes of polynomials with constraints (MR1332893)
1994
 The ProuhetTarryEscott problem revisited (MR1279058)
 Momentmatching and best entropy estimation (MR1288228)
 Markov and Bernstein type inequalities on subsets of [1,1] and [π,π] (MR1278768)
 Chebyshev polynomials and MarkovBernstein type inequalities for rational spaces (MR1299454)
 Müntz systems and orthogonal MüntzLegendre polynomials (MR1227091)
 MarkovBernsteintype inequalities for classes of polynomials with restricted zeros (MR1291056)
 Some cubic modular identities of Ramanujan (MR1243610)
 Exact inequalities for the norms of factors of polynomials (MR1289054)
1993
 The density of rational functions in Markov systems: a counterexample to a conjecture of D. J. Newman (MR1198525)
 On the generating function of the integer part: [nα +γ] (MR1212686)
 An interesting infinite product (MR1244958)
 Some restricted partition functions (MR1242717)
 Lacunary Müntz systems (MR1242750)
 Inequalities for compound mean iterations with logarithmic asymptotes (MR1231502)
 Hypergeometric analogues of the arithmeticgeometric mean iteration (MR1237931)
 Class number three Ramanujan type series for 1/π. Computational complex analysis (MR1222488)
 The usual behavior of rational approximation. II (MR1209968)
1992
 On the denseness of weighted incomplete approximations (MR1240793)
 On the irrationality of certain series (MR1162938)
 Remez, Nikolskii, and Markovtype inequalities for generalized nonnegative polynomials with restricted zeros (MR1164074)
 Strange series and high precision fraud (MR1176589)
 Rational approximation to Lipschitz and Zygmund classes (MR1194026)
 On approximation by trigonometric Lagrange interpolating polynomials. II (MR1155479)
1991
 Notes on lacunary Müntz polynomials (MR1177339)
 Variations on Müntz's theme (MR1127751)
 On the irrationality of ∑(1/(q^{n}+r)) (MR1096442)
 A cubic counterpart of Jacobi's identity and the AGM (MR1010408)
 Quadratically converging rational mean iterations. (MR1088637)
1990
 A remarkable cubic mean iteration (MR1071759)
 A survey of Sylvester's problem and its generalizations (MR1069788)
 Zeros of Chebyshev polynomials in Markov systems (MR1074081)
 Some questions of Erdös and Graham on numbers of the form ∑g_{n}/2^{gn} (MR0990598)
1989
 Pi, Euler numbers, and asymptotic expansions (MR1019148)
 Hypertranscendence of the functional equation g(x^{2})=[g(x)]^{2}+cx (MR0979226)
 On the mean iteration (a,b)← ((a+3b)/4,(√ab +b)/2) (MR0968148)
 Approximating π with Ramanujan's modular equations (MR1016163)
 The density of alternation points in rational approximation (MR0948147)
 Ramanujan, modular equations, and approximations to pi, or How to compute one billion digits of pi (MR0991866)
1988
 More Ramanujantype series for 1/π (MR0938974)
 On the complexity of familiar functions and numbers (MR0967961)
 Padé approximants for the qelementary functions (MR0956175)
 Ramanujan's rational and algebraic series for 1/π (MR0988313)
 Explicit Ramanujantype approximations to pi of high order (MR0983604)
1987
 Quadratic and higher order Padé approximants (MR0899533)
 Unsolved Problems: The Way of All Means (MR1541118)
 Reduced complexity evaluation of hypergeometric functions (MR0892217)
1986
 Quadratic HermitePadé approximation to the exponential function (MR0892157)
 An explicit cubic iteration for π (MR0833837)
 More quadratically converging algorithms for π (MR0815846)
1985
 On the complexity of calculating factorials (MR0800727)
 Rational interpolation to e^{x}. II (MR0783989)
 Markov's inequality for polynomials with real zeros (MR0766524)
1984
 Explicit algebraic nth order approximations to pi (MR0786845)
 The arithmeticgeometric mean and fast computation of elementary functions (MR0750454)
 Cubic and higher order algorithms for π (MR0763041)
 On monochromatic triangles (MR0757616)
 The relationship between the zeros of best approximations and differentiability (MR0760939)
 Sylvester's problem and Motzkin's theorem for countable and compact sets (MR0733410)
 On the behavior of the MLE of the scale parameter of the Student family (MR0764853)
1983
 The relationship between differentiability of a function and the zeros of its best approximations (MR0754361)
 A very rapidly convergent product expansion for π (MR0721199)
 The usual behaviour of rational approximations (MR0703403)
 The Desmic conjecture (MR0704251)
 Rational approximations with real poles to e^{x} and x^{n} (MR0705546)
 Uniform approximation by polynomials with variable exponents (MR0717138)
 On Padé and best rational approximation (MR0681952)
 On Sylvester's problem and Haar spaces (MR0721919)
 Unsolved Problems: A Conjecture Related to Sylvester's Problem (MR1540214)
 Rational approximations to Stieltjes transforms (MR0733943)
1982
 Approximations with negative roots and poles (MR0662161)
 On monochrome lines and hyperplanes (MR0665657)
 Rational interpolation to e^{x} (MR0662162)
 On a method of Newman and a theorem of Bernstein (MR0647709)
 The size of {x:r′_{n}/r_{n} ≥ 1} and lower bounds for e^{x}r_{n} (MR0673858)
1981
 Approximation of x^{n} by reciprocals of polynomials (MR0641960)
 Markov's and Bernstein's inequalities on disjoint intervals (MR0608865)
1980
 Approximations by rational functions with positive coefficients (MR0568377)
 Rational functions with positive coefficients, polynomials and uniform approximations (MR0595813)
 Inequalities and inverse theorems in restricted rational approximation theory (MR0571930)
1978
 Arbitrarily slow rational approximations on the positive real line (MR0509563)