## Borwein, Peter Benjamin

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 Author ID: borwein.peter-benjamin Published as: Borwein, Peter; Borwein, Peter B.; Borwein, P. B.; Borwein, P.; Borwein, Peter Benjamin External Links: MGP · Wikidata · dblp · GND · IdRef
 Documents Indexed: 183 Publications since 1978, including 8 Books 7 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 85 Co-Authors with 146 Joint Publications 1,611 Co-Co-Authors
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### Co-Authors

 44 single-authored 39 Borwein, Jonathan Michael 36 Erdélyi, Tamás 10 Mossinghoff, Michael J. 9 Choi, Kwok-Kwong Stephen 8 Choi, Stephen Kwok-Kwong 7 Ferguson, Ron 6 Bailey, David Harold 4 Hare, Kevin G. 4 Pinner, Christopher G. 4 Zhou, Ping 3 Berggren, John Lennart 3 Boyd, David William 3 Corless, Robert Malcolm 3 Garvan, Frank G. 3 Girgensohn, Roland 3 Jankauskas, Jonas 3 Jörgenson, Loki 3 Saff, Edward Barry 2 Beaucoup, Franck 2 Borwein, David 2 Chen, Weiyu 2 Coons, Michael 2 Dilcher, Karl 2 Ferguson, R. A. 2 Kós, Géza 2 Lockhart, Richard A. 2 Parnes, Sheldon 2 Plouffe, Simon 2 Pritsker, Igor E. 2 Shekhtman, Boris 2 van der Waall, Alexa 2 Zhang, John Z. H. 2 Zhou, Songping 1 Alimadad, Azadeh 1 Aragón Artacho, Francisco Javier 1 Baishanski, Bogdan M. 1 Bauschke, Heinz H. 1 Bell, Jason P. 1 Belshaw, Adrian 1 Borwein, Alex 1 Cheney, Elliott Ward jun. 1 Chu, Frank Pok Man 1 1 Cuyt, Annie A. M. 1 Dabbaghian, Vahid 1 Dickmeis, Werner 1 Dobrowolski, Edward 1 Drakes, Chiaka 1 Dykshoorn, Willem 1 Fee, Greg J. 1 Ganguli, Himadri 1 Ghaseminejad, Amir H. 1 Gonska, Heinz Herbert 1 Gusev, Yuri V. 1 Hare, Warren L. 1 Hobart, Joe 1 Ingalls, Colin 1 Jakimovski, Amnon 1 Jedwab, Jonathan 1 Jeffrey, David J. 1 Kaltofen, Erich L. 1 Kalugin, German A. 1 Knauer, Joshua 1 Kroó, András 1 Lewis, Adrian S. 1 Li, Jenny X. 1 Liljedahl, Peter 1 Lisoněk, Petr 1 Littmann, Friedrich 1 Loring, Terry A. 1 Martin, Greg 1 Mercer, Idris David 1 Mitrović-Minić, Snežana 1 Moser, William Oscar Jules 1 Nessel, Rolf Joachim 1 Peetre, Jaak 1 Percival, Colin 1 Rakhmanov, Evgenij Andreevich 1 Richmond, L. Bruce 1 Rooney, Brendan 1 Rutherford, Alexander 1 Samuels, Charles L. 1 Schoenberg, Isaac Jacob 1 Sinclair, Nathalie 1 Stenger, Frank 1 Théra, Michel A. 1 Vaaler, Jeffrey D. 1 van Wickeren, Erich 1 Vanderwerff, Jon D. 1 Vásárhelyi, Krisztina 1 Vertesi, Les 1 Vértesi, Péter 1 Weirathmueller, Andrea 1 Wolkowicz, Henry 1 Yazdani, Soroosh 1 Zhai, Helen
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### Serials

 18 Proceedings of the American Mathematical Society 14 Mathematics of Computation 14 Journal of Approximation Theory 12 Constructive Approximation 8 American Mathematical Monthly 8 Canadian Journal of Mathematics 8 Transactions of the American Mathematical Society 6 Canadian Mathematical Bulletin 5 Journal of Mathematical Analysis and Applications 5 Journal of the London Mathematical Society. Second Series 3 The Mathematical Intelligencer 3 Acta Arithmetica 3 Journal of Combinatorial Theory. Series A 3 Journal of Number Theory 3 Experimental Mathematics 2 IEEE Transactions on Information Theory 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 BIT 2 Bulletin of the London Mathematical Society 2 Mathematika 2 Pacific Journal of Mathematics 2 SIAM Review 2 Annals of Mathematics. Second Series 2 Canadian Mathematical Society Series of Monographs and Advanced Texts 2 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Israel Journal of Mathematics 1 Rocky Mountain Journal of Mathematics 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 The Journal of the Indian Mathematical Society. New Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Journal of Algorithms 1 Acta Mathematica Hungarica 1 Journal of the American Mathematical Society 1 Aequationes Mathematicae 1 Communications in Statistics. Theory and Methods 1 L’Enseignement Mathématique. 2e Série 1 Pokroky Matematiky, Fyziky & Astronomie 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Indagationes Mathematicae. New Series 1 Advances in Computational Mathematics 1 Integral Transforms and Special Functions 1 The Ramanujan Journal 1 LMS Journal of Computation and Mathematics 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 JP Journal of Algebra, Number Theory and Applications 1 International Journal of Number Theory 1 CMS Conference Proceedings 1 ACM Communications in Computer Algebra 1 Springer Proceedings in Mathematics & Statistics 1 MAA Spectrum
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### Fields

 90 Number theory (11-XX) 71 Approximations and expansions (41-XX) 39 Functions of a complex variable (30-XX) 25 Special functions (33-XX) 21 Real functions (26-XX) 13 General and overarching topics; collections (00-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 13 Numerical analysis (65-XX) 11 History and biography (01-XX) 11 Information and communication theory, circuits (94-XX) 8 Computer science (68-XX) 7 Combinatorics (05-XX) 7 Field theory and polynomials (12-XX) 7 Geometry (51-XX) 6 Difference and functional equations (39-XX) 6 Sequences, series, summability (40-XX) 4 Convex and discrete geometry (52-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

167 Publications have been cited 2,152 times in 1,490 Documents Cited by Year
Polynomials and polynomial inequalities. Zbl 0840.26002
Borwein, Peter; Erdélyi, Tamás
1995
Pi and the AGM. A study in analytic number theory and computational complexity. Zbl 0611.10001
Borwein, Jonathan M.; Borwein, Peter B.
1987
A cubic counterpart of Jacobi’s identity and the AGM. Zbl 0725.33014
Borwein, J. M.; Borwein, P. B.
1991
Ramanujan’s rational and algebraic series for $$1/\pi$$. Zbl 0699.10044
Borwein, J. M.; Borwein, P. B.
1987
Computational excursions in analysis and number theory. Zbl 1020.12001
Borwein, Peter
2002
On the rapid computation of various polylogarithmic constants. Zbl 0879.11073
Bailey, David; Borwein, Peter; Plouffe, Simon
1997
Some cubic modular identities of Ramanujan. Zbl 0799.33012
Borwein, J. M.; Borwein, P. B.; Garvan, F. G.
1994
Müntz systems and orthogonal Müntz-Legendre polynomials. Zbl 0799.41015
Borwein, Peter; Erdélyi, Tamás; Zhang, John
1994
Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi. Zbl 0672.10017
Borwein, J. M.; Borwein, P. B.; Bailey, D. H.
1989
The arithmetic-geometric mean and fast computation of elementary functions. Zbl 0557.65009
Borwein, J. M.; Borwein, P. B.
1984
A survey of Sylvester’s problem and its generalizations. Zbl 0717.52013
Borwein, P.; Moser, W. O. J.
1990
Pi and the AGM. A study in analytic number theory and computational complexity. Zbl 0903.11001
Borwein, Jonathan M.; Borwein, Peter B.
1998
The Prouhet-Tarry-Escott problem revisited. Zbl 0810.11016
Borwein, Peter; Ingalls, Colin
1994
On the irrationality of $$\sum (1/(q^ n+r))$$. Zbl 0718.11029
Borwein, Peter B.
1991
The integer Chebyshev problem. Zbl 0859.11044
Borwein, Peter; Erdélyi, Tamás
1996
Lehmer’s problem for polynomials with odd coefficients. Zbl 1172.11034
Borwein, Peter; Dobrowolski, Edward; Mossinghoff, Michael J.
2007
Sharp extensions of Bernstein’s inequality to rational spaces. Zbl 0869.41010
Borwein, Peter; Erdélyi, Tamás
1996
Littlewood-type problems on $$[0,1]$$. Zbl 1039.11046
Borwein, Peter; Erdélyi, Tamás; Kós, Géza
1999
On the irrationality of certain series. Zbl 0779.11027
Borwein, Peter B.
1992
Generalizations of Müntz’s theorem via a Remez-type inequality for Müntz spaces. Zbl 0864.41014
Borwein, Peter; Erdélyi, Tamás
1997
Inequalities for compound mean iterations with logarithmic asymptotes. Zbl 0783.33001
Borwein, Jonathan M.; Borwein, Peter B.
1993
Multiple roots of $$[-1,1]$$ power series. Zbl 0922.30004
Beaucoup, Franck; Borwein, Peter; Boyd, David W.; Pinner, Christopher
1998
The full Müntz theorem in $$C[0,1]$$ and $$L_ 1[0,1]$$. Zbl 0854.41015
Borwein, Peter; Erdélyi, Tamás
1996
On the zeros of polynomials with restricted coefficients. Zbl 0906.30005
Borwein, Peter; Erdélyi, Tamás
1997
The Riemann hypothesis. A resource for the afficionado and virtuoso alike. Zbl 1132.11047
2007
Chebyshev polynomials and Markov-Bernstein type inequalities for rational spaces. Zbl 0815.41013
Borwein, Peter; Erdélyi, Tamás; Zhang, John
1994
Padé approximants for the q-elementary functions. Zbl 0685.41015
Borwein, Peter B.
1988
Some computations on the spectra of Pisot and Salem numbers. Zbl 1037.11065
Borwein, Peter; Hare, Kevin G.
2002
Making sense of experimental mathematics. Zbl 0874.00027
Borwein, J.; Borwein, P.; Girgensohn, R.; Parnes, S.
1996
The quest for pi. Zbl 0878.11002
Bailey, D. H.; Borwein, J. M.; Borwein, P. B.; Plouffe, S.
1997
The expected $$L_{p}$$ norm of random polynomials. Zbl 0999.30004
Borwein, Peter; Lockhart, Richard
2001
Class number three Ramanujan type series for $$1/\pi$$. Zbl 0818.65010
Borwein, J. M.; Borwein, P. B.
1993
Borwein, Peter B.
1986
On the generating function of the integer part: $$[n\alpha{}+ \gamma{}]$$. Zbl 0778.11039
Borwein, J. M.; Borwein, P. B.
1993
Markov’s inequality for polynomials with real zeros. Zbl 0564.26003
Borwein, Peter
1985
More Ramanujan-type series for 1/$$\pi$$. Zbl 0652.10019
Borwein, J. M.; Borwein, P. B.
1988
An efficient algorithm for the Riemann zeta function. Zbl 0984.11067
Borwein, P.
2000
Completely multiplicative functions taking values in $$\{-1,1\}$$. Zbl 1222.11111
Borwein, Peter; Choi, Stephen K. K.; Coons, Michael
2010
A complete description of Golay pairs for lengths up to 100. Zbl 1052.11019
Borwein, P. B.; Ferguson, R. A.
2004
Polynomials with coefficients from a finite set. Zbl 1158.30002
Borwein, Peter; Erdélyi, Tamás; Littmann, Friedrich
2008
Pi, Euler numbers, and asymptotic expansions. Zbl 0711.11009
Borwein, J. M.; Borwein, P. B.; Dilcher, K.
1989
Giuga’s conjecture on primality. Zbl 0860.11003
Borwein, D.; Borwein, J. M.; Borwein, P. B.; Girgensohn, R.
1996
Sign changes in sums of the Liouville function. Zbl 1198.11090
Borwein, Peter; Ferguson, Ron; Mossinghoff, Michael J.
2008
Polynomials with height 1 and prescribed vanishing at 1. Zbl 0999.12001
Borwein, Peter; Mossinghoff, Michael J.
2000
Polynomials with $$\{0,+1,-1\}$$ coefficients and a root close to a given point. Zbl 0901.11022
Borwein, Peter; Pinner, Christopher
1997
Pi: a source book. 3rd ed. Zbl 1054.11001
2004
On the zeros of cosine polynomials: solution to a problem of Littlewood. Zbl 1186.11045
Borwein, Peter Benjamin; Erdélyi, Tamás; Ferguson, Ron; Lockhart, Richard
2008
Zeros of partial sums of the Riemann zeta function. Zbl 1219.11126
Borwein, Peter; Fee, Greg; Ferguson, Ron; van der Waall, Alexa
2007
An old conjecture of Erdős-Turán on additive bases. Zbl 1093.11018
Borwein, Peter; Choi, Stephen; Chu, Frank
2006
Littlewood-type problems on subarcs of the unit circle. Zbl 0930.30005
Borwein, Peter; Erdélyi, Tamás
1997
The density of alternation points in rational approximation. Zbl 0688.41018
Borwein, P. B.; Króo, A.; Grothmann, R.; Saff, E. B.
1989
Transcendence of power series for some number theoretic functions. Zbl 1236.11063
Borwein, Peter; Coons, Michael
2009
Incomplete rational approximation in the complex plane. Zbl 0820.41013
Borwein, P. B.; Chen, Weiyu
1995
Explicit merit factor formulae for Fekete and Turyn polynomials. Zbl 1010.11017
Borwein, Peter; Choi, Kwok-Kwong Stephen
2002
The arc length of the lemniscate $$\{| p(z)| =1\}$$. Zbl 0821.31002
Borwein, Peter
1995
Müntz spaces and Remez inequalities. Zbl 0814.41013
Borwein, Peter; Erdélyi, Tamás
1995
Barker sequences and flat polynomials. Zbl 1266.11051
Borwein, Peter; Mossinghoff, Michael
2008
Stieltjes and other integral representations for functions of Lambert W. Zbl 1258.33015
Kalugin, German A.; Jeffrey, David J.; Corless, Robert M.; Borwein, Peter B.
2012
A remarkable cubic mean iteration. Zbl 0709.30020
Borwein, J. M.; Borwein, P. B.
1990
On the complexity of familiar functions and numbers. Zbl 0686.68029
Borwein, J. M.; Borwein, P. B.
1988
On cyclotomic polynomials with $$\pm 1$$ coefficients. Zbl 0947.11031
Borwein, Peter; Choi, Kwok-Kwong Stephen
1999
Rudin-Shapiro-like polynomials in $$L_4$$. Zbl 1042.11046
Borwein, Peter; Mossinghoff, Michael
2000
Pi: a source book. Zbl 0876.11001
1997
Power series with restricted coefficients and a root on a given ray. Zbl 0889.30006
Beaucoup, Franck; Borwein, Peter; Boyd, David W.; Pinner, Christopher
1998
Exact inequalities for the norms of factors of polynomials. Zbl 0820.30006
Borwein, Peter B.
1994
Lower bounds for the number of zeros of cosine polynomials in the period: a problem of Littlewood. Zbl 1124.41009
Borwein, Peter; Erdélyi, Tamás
2007
Strange series and high precision fraud. Zbl 0762.40003
Borwein, J. M.; Borwein, P. B.
1992
Zeros of Chebyshev polynomials in Markov systems. Zbl 0733.41012
Borwein, Peter
1990
Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros. Zbl 0816.41012
Borwein, Peter; Erdélyi, Tamás
1994
Monic integer Chebyshev problem. Zbl 1054.11018
Borwein, P. B.; Pinner, C. G.; Pritsker, I. E.
2003
Visible structures in number theory. Zbl 1160.11300
Borwein, Peter; Jörgenson, Loki
2001
The Mahler measure of polynomials with odd coefficients. Zbl 1143.11349
Borwein, Peter; Hare, Kevin G.; Mossinghoff, Michael J.
2004
Nikolskii-type inequalities for shift invariant function spaces. Zbl 1113.41017
Borwein, Peter; Erdélyi, Tamás
2006
The way of all means. Zbl 0628.26003
Borwein, J. M.; Borwein, P. B.
1987
Variations on Müntz’s theme. Zbl 0758.41027
Borwein, Peter B.
1991
The $$L_ p$$ version of Newman’s inequality for lacunary polynomials. Zbl 0840.41008
Borwein, Peter; Erdélyi, Tamás
1996
A sharp Bernstein-type inequality for exponential sums. Zbl 0851.41011
Borwein, Peter; Erdélyi, Tamás
1996
Merit factors of character polynomials. Zbl 1011.11059
Borwein, Peter; Choi, Kwok-Kwong Stephen
2000
Wieferich pairs and Barker sequences. II. Zbl 1355.11018
Borwein, Peter; Mossinghoff, Michael J.
2014
Merit factors of polynomials formed by Jacobi symbols. Zbl 0964.11020
Borwein, Peter; Choi, Kwok-Kwong Stephen
2001
General forms for minimal spectral values for a class of quadratic Pisot numbers. Zbl 1094.11038
Borwein, Peter; Hare, Kevin G.
2003
Walking on real numbers. Zbl 1282.11088
Aragón Artacho, Francisco J.; Bailey, David H.; Borwein, Jonathan M.; Borwein, Peter B.
2013
On the complexity of calculating factorials. Zbl 0576.68027
Borwein, Peter B.
1985
The relationship between the zeros of best approximations and differentiability. Zbl 0552.41019
Borwein, Peter B.
1984
On the mean iteration $$(a,b)\leftarrow ((a+3b)/4,(\sqrt{ab}+b)/2)$$. Zbl 0675.30023
Borwein, J. M.; Borwein, P. B.
1989
Pi: a source book. 2nd ed. Zbl 1039.11001
2000
Pointwise Remez- and Nikolskii-type inequalities for exponential sums. Zbl 0949.41006
Borwein, Peter; Erdélyi, Tamás
2000
Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros. Zbl 0755.41017
Borwein, Peter; Erdélyi, Tamás
1992
Notes on lacunary Müntz polynomials. Zbl 0762.41009
Borwein, Peter; Erdély, Tamás
1991
On Littlewood polynomials with prescribed number of zeros inside the unit disk. Zbl 1320.11097
Borwein, Peter; Choi, Stephen; Ferguson, Ron; Jankauskas, Jonas
2015
Newman’s inequality for Müntz polynomials on positive intervals. Zbl 0853.41008
Borwein, Peter; Erdélyi, Tamás
1996
Rational approximation with varying weights I. Zbl 0870.41010
Borwein, P.; Rakhmanov, E. A.; Saff, E. B.
1996
An extremal property of Fekete polynomials. Zbl 0987.11010
Borwein, Peter; Choi, Kwok-Kwong Stephen; Yazdani, Soroosh
2001
Hypergeometric analogues of the arithmetic-geometric mean iteration. Zbl 0785.33001
Borwein, J.; Borwein, P.; Garvan, F.
1993
An interesting infinite product. Zbl 0793.40006
Borwein, Peter; Dykshoorn, Willem
1993
Moment-matching and best entropy estimation. Zbl 0813.41018
1994
Computational investigations of the Prouhet-Tarry-Escott problem. Zbl 1026.11094
Borwein, Peter; Lisoněk, Petr; Percival, Colin
2003
Markov- and Bernstein-type inequalities for polynomials with restricted coefficients. Zbl 0902.41012
Borwein, Peter; Erdélyi, Tamás
1997
The average norm of polynomials of fixed height. Zbl 1198.11030
Borwein, Peter; Choi, Kwok-Kwong Stephen
2007
Growth of the product $$\prod_{j=1}^n (1-x^{a_j})$$. Zbl 0918.11054
Bell, J. P.; Borwein, P. B.; Richmond, L. B.
1998
On Littlewood polynomials with prescribed number of zeros inside the unit disk. Zbl 1320.11097
Borwein, Peter; Choi, Stephen; Ferguson, Ron; Jankauskas, Jonas
2015
Wieferich pairs and Barker sequences. II. Zbl 1355.11018
Borwein, Peter; Mossinghoff, Michael J.
2014
Walking on real numbers. Zbl 1282.11088
Aragón Artacho, Francisco J.; Bailey, David H.; Borwein, Jonathan M.; Borwein, Peter B.
2013
The multiplicity of the zero at 1 of polynomials with constrained coefficients. Zbl 1284.11054
Borwein, Peter; Erdélyi, Tamás; Kós, Géza
2013
Extremal Mahler measures and $$L_s$$ norms of polynomials related to Barker sequences. Zbl 1272.11041
Borwein, Peter; Choi, Stephen; Jankauskas, Jonas
2013
Champernowne’s number, strong normality, and the X chromosome. Zbl 1283.11108
2013
Computational and analytical mathematics. In Honor of Jonathan Borwein’s 60th birthday. Selected papers based on the presentations at the workshop, also known as JonFest, Simon Fraser University, BC, Canada, May 16–20, 2011. Zbl 1276.00018
2013
A note on Barker polynomials. Zbl 1333.11030
Borwein, Peter; Erdélyi, Tamás
2013
Stieltjes and other integral representations for functions of Lambert W. Zbl 1258.33015
Kalugin, German A.; Jeffrey, David J.; Corless, Robert M.; Borwein, Peter B.
2012
On a class of polynomials related to Barker sequences. Zbl 1329.11022
Borwein, Peter; Choi, Stephen; Jankauskas, Jonas
2012
The extraordinary power of division in straight line programs. Zbl 1271.11118
Borwein, Peter; Hobart, Joe
2012
Completely multiplicative functions taking values in $$\{-1,1\}$$. Zbl 1222.11111
Borwein, Peter; Choi, Stephen K. K.; Coons, Michael
2010
Experimental and computational mathematics: selected writings. Zbl 1225.01096
Borwein, Jonathan; Borwein, Peter
2010
Transcendence of power series for some number theoretic functions. Zbl 1236.11063
Borwein, Peter; Coons, Michael
2009
The multivariate integer Chebyshev problem. Zbl 1246.11075
Borwein, P. B.; Pritsker, I. E.
2009
Polynomials with coefficients from a finite set. Zbl 1158.30002
Borwein, Peter; Erdélyi, Tamás; Littmann, Friedrich
2008
Sign changes in sums of the Liouville function. Zbl 1198.11090
Borwein, Peter; Ferguson, Ron; Mossinghoff, Michael J.
2008
On the zeros of cosine polynomials: solution to a problem of Littlewood. Zbl 1186.11045
Borwein, Peter Benjamin; Erdélyi, Tamás; Ferguson, Ron; Lockhart, Richard
2008
Barker sequences and flat polynomials. Zbl 1266.11051
Borwein, Peter; Mossinghoff, Michael
2008
Expected norms of zero-one polynomials. Zbl 1173.11015
Borwein, Peter; Choi, Kwok-Kwong Stephen; Mercer, Idris
2008
The merit factor problem. Zbl 1266.11050
Borwein, Peter; Ferguson, Ron; Knauer, Joshua
2008
Lehmer’s problem for polynomials with odd coefficients. Zbl 1172.11034
Borwein, Peter; Dobrowolski, Edward; Mossinghoff, Michael J.
2007
The Riemann hypothesis. A resource for the afficionado and virtuoso alike. Zbl 1132.11047
2007
Zeros of partial sums of the Riemann zeta function. Zbl 1219.11126
Borwein, Peter; Fee, Greg; Ferguson, Ron; van der Waall, Alexa
2007
Lower bounds for the number of zeros of cosine polynomials in the period: a problem of Littlewood. Zbl 1124.41009
Borwein, Peter; Erdélyi, Tamás
2007
The average norm of polynomials of fixed height. Zbl 1198.11030
Borwein, Peter; Choi, Kwok-Kwong Stephen
2007
Irreducible polynomials and Barker sequences. Zbl 1322.68271
Borwein, Peter; Kaltofen, Erich; Mossinghoff, Michael J.
2007
Generalizations of Gonçalves’ inequality. Zbl 1126.30006
Borwein, Peter; Mossinghoff, Michael J.; Vaaler, Jeffrey D.
2007
An old conjecture of Erdős-Turán on additive bases. Zbl 1093.11018
Borwein, Peter; Choi, Stephen; Chu, Frank
2006
Nikolskii-type inequalities for shift invariant function spaces. Zbl 1113.41017
Borwein, Peter; Erdélyi, Tamás
2006
Norms of cyclotomic Littlewood polynomials. Zbl 1080.11020
Borwein, Peter; Choi, Stephen Kwok-Kwong; Ferguson, Ron
2005
Polyphase sequences with low autocorrelation. Zbl 1267.94023
Borwein, Peter B.; Ferguson, R. A.
2005
Explicit construction of general multivariate Padé approximants to an Appell function. Zbl 1085.41010
Borwein, P. B.; Cuyt, A.; Zhou, P.
2005
A complete description of Golay pairs for lengths up to 100. Zbl 1052.11019
Borwein, P. B.; Ferguson, R. A.
2004
Pi: a source book. 3rd ed. Zbl 1054.11001
2004
The Mahler measure of polynomials with odd coefficients. Zbl 1143.11349
Borwein, Peter; Hare, Kevin G.; Mossinghoff, Michael J.
2004
Binary sequences with merit factor greater than 6.34. Zbl 1267.94024
Borwein, Peter; Choi, Kwok-Kwong Stephen; Jedwab, Jonathan
2004
Monic integer Chebyshev problem. Zbl 1054.11018
Borwein, P. B.; Pinner, C. G.; Pritsker, I. E.
2003
General forms for minimal spectral values for a class of quadratic Pisot numbers. Zbl 1094.11038
Borwein, Peter; Hare, Kevin G.
2003
Computational investigations of the Prouhet-Tarry-Escott problem. Zbl 1026.11094
Borwein, Peter; Lisoněk, Petr; Percival, Colin
2003
Newman polynomials with prescribed vanishing and integer sets with distinct subset sums. Zbl 1023.11008
Borwein, Peter; Mossinghoff, Michael J.
2003
Non-trivial quadratic approximations to zero of a family of cubic Pisot numbers. Zbl 1083.11044
Borwein, Peter; Hare, Kevin G.
2003
Lower bounds for the merit factors of trigonometric polynomials from Littlewood classes. Zbl 1038.42002
Borwein, Peter; Erdélyi, Tamás
2003
Computational excursions in analysis and number theory. Zbl 1020.12001
Borwein, Peter
2002
Some computations on the spectra of Pisot and Salem numbers. Zbl 1037.11065
Borwein, Peter; Hare, Kevin G.
2002
Explicit merit factor formulae for Fekete and Turyn polynomials. Zbl 1010.11017
Borwein, Peter; Choi, Kwok-Kwong Stephen
2002
Paul Erdős and polynomials. Zbl 1031.11011
Borwein, P.
2002
The expected $$L_{p}$$ norm of random polynomials. Zbl 0999.30004
Borwein, Peter; Lockhart, Richard
2001
Visible structures in number theory. Zbl 1160.11300
Borwein, Peter; Jörgenson, Loki
2001
Merit factors of polynomials formed by Jacobi symbols. Zbl 0964.11020
Borwein, Peter; Choi, Kwok-Kwong Stephen
2001
An extremal property of Fekete polynomials. Zbl 0987.11010
Borwein, Peter; Choi, Kwok-Kwong Stephen; Yazdani, Soroosh
2001
Trigonometric polynomials with many real zeros and a Littlewood-type problem. Zbl 0968.41008
Borwein, Peter; Erdélyi, Tamás
2001
An efficient algorithm for the Riemann zeta function. Zbl 0984.11067
Borwein, P.
2000
Polynomials with height 1 and prescribed vanishing at 1. Zbl 0999.12001
Borwein, Peter; Mossinghoff, Michael J.
2000
Rudin-Shapiro-like polynomials in $$L_4$$. Zbl 1042.11046
Borwein, Peter; Mossinghoff, Michael
2000
Merit factors of character polynomials. Zbl 1011.11059
Borwein, Peter; Choi, Kwok-Kwong Stephen
2000
Pi: a source book. 2nd ed. Zbl 1039.11001
2000
Pointwise Remez- and Nikolskii-type inequalities for exponential sums. Zbl 0949.41006
Borwein, Peter; Erdélyi, Tamás
2000
Markov-Bernstein type inequalities under Littlewood-type coefficient constraints. Zbl 1011.26010
Borwein, Peter; Erdélyi, Tamás
2000
The amazing number $$\pi$$. Zbl 1173.01300
Borwein, Peter
2000
Littlewood-type problems on $$[0,1]$$. Zbl 1039.11046
Borwein, Peter; Erdélyi, Tamás; Kós, Géza
1999
On cyclotomic polynomials with $$\pm 1$$ coefficients. Zbl 0947.11031
Borwein, Peter; Choi, Kwok-Kwong Stephen
1999
On the irrationality of a certain $$q$$ series. Zbl 0926.11051
Borwein, Peter B.; Zhou, Ping
1999
Pi and the AGM. A study in analytic number theory and computational complexity. Zbl 0903.11001
Borwein, Jonathan M.; Borwein, Peter B.
1998
Multiple roots of $$[-1,1]$$ power series. Zbl 0922.30004
Beaucoup, Franck; Borwein, Peter; Boyd, David W.; Pinner, Christopher
1998
Power series with restricted coefficients and a root on a given ray. Zbl 0889.30006
Beaucoup, Franck; Borwein, Peter; Boyd, David W.; Pinner, Christopher
1998
Growth of the product $$\prod_{j=1}^n (1-x^{a_j})$$. Zbl 0918.11054
Bell, J. P.; Borwein, P. B.; Richmond, L. B.
1998
Some old problems on polynomials with integer coefficients. Zbl 0930.12001
Borwein, Peter
1998
Müntz’s theorem on compact subsets of positive measure. Zbl 0901.41005
Borwein, Peter; Erdélyi, Tamás
1998
A Remez-type inequality for non-dense Müntz spaces with explicit bound. Zbl 0904.41006
Borwein, Peter; Erdélyi, Tamás
1998
On the rapid computation of various polylogarithmic constants. Zbl 0879.11073
Bailey, David; Borwein, Peter; Plouffe, Simon
1997
Generalizations of Müntz’s theorem via a Remez-type inequality for Müntz spaces. Zbl 0864.41014
Borwein, Peter; Erdélyi, Tamás
1997
On the zeros of polynomials with restricted coefficients. Zbl 0906.30005
Borwein, Peter; Erdélyi, Tamás
1997
The quest for pi. Zbl 0878.11002
Bailey, D. H.; Borwein, J. M.; Borwein, P. B.; Plouffe, S.
1997
Polynomials with $$\{0,+1,-1\}$$ coefficients and a root close to a given point. Zbl 0901.11022
Borwein, Peter; Pinner, Christopher
1997
Littlewood-type problems on subarcs of the unit circle. Zbl 0930.30005
Borwein, Peter; Erdélyi, Tamás
1997
Pi: a source book. Zbl 0876.11001
1997
Markov- and Bernstein-type inequalities for polynomials with restricted coefficients. Zbl 0902.41012
Borwein, Peter; Erdélyi, Tamás
1997
What is organic mathematics? Zbl 1053.00506
Borwein, Jonathan M.; Borwein, Peter B.; Corless, Robert M.; Jörgenson, Loki; Sinclair, Nathalie
1997
The integer Chebyshev problem. Zbl 0859.11044
Borwein, Peter; Erdélyi, Tamás
1996
Sharp extensions of Bernstein’s inequality to rational spaces. Zbl 0869.41010
Borwein, Peter; Erdélyi, Tamás
1996
The full Müntz theorem in $$C[0,1]$$ and $$L_ 1[0,1]$$. Zbl 0854.41015
Borwein, Peter; Erdélyi, Tamás
1996
Making sense of experimental mathematics. Zbl 0874.00027
Borwein, J.; Borwein, P.; Girgensohn, R.; Parnes, S.
1996
Giuga’s conjecture on primality. Zbl 0860.11003
Borwein, D.; Borwein, J. M.; Borwein, P. B.; Girgensohn, R.
1996
The $$L_ p$$ version of Newman’s inequality for lacunary polynomials. Zbl 0840.41008
Borwein, Peter; Erdélyi, Tamás
1996
A sharp Bernstein-type inequality for exponential sums. Zbl 0851.41011
Borwein, Peter; Erdélyi, Tamás
1996
Newman’s inequality for Müntz polynomials on positive intervals. Zbl 0853.41008
Borwein, Peter; Erdélyi, Tamás
1996
Rational approximation with varying weights I. Zbl 0870.41010
Borwein, P.; Rakhmanov, E. A.; Saff, E. B.
1996
Questions about polynomials with $$\{ 0,-1,+1\}$$ coefficients: Research problems 96-3. Zbl 0877.41013
Borwein, Peter; Erdélyi, Tamás
1996
Polynomials and polynomial inequalities. Zbl 0840.26002
Borwein, Peter; Erdélyi, Tamás
1995
Incomplete rational approximation in the complex plane. Zbl 0820.41013
Borwein, P. B.; Chen, Weiyu
1995
The arc length of the lemniscate $$\{| p(z)| =1\}$$. Zbl 0821.31002
Borwein, Peter
1995
Müntz spaces and Remez inequalities. Zbl 0814.41013
Borwein, Peter; Erdélyi, Tamás
1995
Zeros of iterated integrals of polynomials. Zbl 0843.30007
Borwein, Peter B.; Chen, Weiyu; Dilcher, Karl
1995
Upper bounds for the derivative of exponential sums. Zbl 0829.41013
Borwein, Peter; Erdélyi, Tamás
1995
Markov and Bernstein type inequalities in $$L_ p$$ for classes of polynomials with constraints. Zbl 0826.41017
Borwein, Peter; Erdélyi, Tamás
1995
Dense Markov spaces and unbounded Bernstein inequalities. Zbl 0865.41015
Borwein, Peter; Erdélyi, Tamás
1995
Some cubic modular identities of Ramanujan. Zbl 0799.33012
Borwein, J. M.; Borwein, P. B.; Garvan, F. G.
1994
Müntz systems and orthogonal Müntz-Legendre polynomials. Zbl 0799.41015
Borwein, Peter; Erdélyi, Tamás; Zhang, John
1994
The Prouhet-Tarry-Escott problem revisited. Zbl 0810.11016
Borwein, Peter; Ingalls, Colin
1994
...and 67 more Documents
all top 5

### Cited by 1,602 Authors

 60 Erdélyi, Tamás 53 Borwein, Peter Benjamin 34 Chu, Yuming 28 Borwein, Jonathan Michael 21 Pritsker, Igor E. 20 Bailey, David Harold 18 Lubinsky, Doron S. 17 Chan, Heng Huat 15 Wang, Miaokun 15 Zudilin, Wadim 14 Qiu, Songliang 13 Kroó, András 13 Xu, Ce 11 Hare, Kevin G. 11 Mossinghoff, Michael J. 11 Yang, Zhenhang 10 Cooper, Shaun 10 Guillera, Jesús 10 Neuman, Edward 10 Saff, Edward Barry 10 Samuels, Charles L. 10 Zhang, Xiaohui 9 Coons, Michael 9 Matkowski, Janusz 8 Andrievskii, Vladimir V. 8 Chu, Wenchang 8 Crandall, Richard E. 8 Ma, Xiaoyan 8 Pinner, Christopher G. 8 Zhou, Ping 7 Choi, Kwok-Kwong Stephen 7 Driver, Kathy A. 7 Jankauskas, Jonas 7 Moll, Victor Hugo 7 Vuorinen, Matti Keijo Kustaa 7 Wan, James Gu Feng 7 Wielonsky, Franck 7 Wu, Qiang 7 Zhao, Tiehong 6 Alzer, Horst 6 Berndt, Bruce Carl 6 Chen, Chaoping 6 Dubickas, Artūras 6 Dvir, Zeev 6 Hančl, Jaroslav 6 Kalmykov, Sergeĭ Ivanovich 6 Rhin, Georges 6 Richards, Kendall C. 6 Schmidt, Kai-Uwe 6 Van Assche, Walter 5 Agarwal, Ravi P. 5 Ait-Haddou, Rachid 5 Allouche, Jean-Paul Simon 5 Anderson, Glen Douglas 5 Baranov, Anton D. 5 Barnard, Roger W. 5 Baruah, Nayandeep Deka 5 Beliakov, Gleb 5 Berenhaut, Kenneth S. 5 Chen, Yonggao 5 Chua, Kok Seng 5 Corless, Robert Malcolm 5 Deng, Guantie 5 Duverney, Daniel 5 Flammang, Valérie 5 Ganzburg, Michael Iosifovich 5 Kofanov, V. A. 5 Mc Laughlin, James G. 5 Mir, Abdullah 5 Navascués, María Antonia 5 Pijeira-Cabrera, Héctor 5 Qian, Weimao 5 Shen, Lichien 5 Solé, Patrick 5 Solomyak, Boris 5 Sondow, Jonathan D. 5 Song, Yingqing 5 Straub, Armin 5 Väänänen, Keijo O. 5 Wang, Liuquan 5 Zarouf, Rachid 4 Alam, Ihab Al 4 Bell, Jason P. 4 Blatt, Hans-Peter 4 Bundschuh, Peter 4 Chamberland, Marc 4 Choi, Stephen Kwok-Kwong 4 Choudhry, Ajai 4 Đoković, Dragomir Ž. 4 Dubinin, Vladimir N. 4 Faulhuber, Markus 4 Grau, José María 4 Hirschhorn, Michael D. 4 Huber, Tim 4 Jarczyk, Justyna 4 Jiang, Yueping 4 Kotsireas, Ilias S. 4 Lefèvre, Pascal 4 Liu, Zhi-Guo 4 Long, Boyong ...and 1,502 more Authors
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### Cited in 326 Serials

 101 Journal of Approximation Theory 87 Journal of Mathematical Analysis and Applications 72 The Ramanujan Journal 63 Journal of Number Theory 59 Mathematics of Computation 45 Proceedings of the American Mathematical Society 38 Transactions of the American Mathematical Society 35 Journal of Computational and Applied Mathematics 28 Constructive Approximation 24 International Journal of Number Theory 20 Applied Mathematics and Computation 20 Journal of Inequalities and Applications 19 Advances in Mathematics 19 Experimental Mathematics 18 Journal de Théorie des Nombres de Bordeaux 17 Rocky Mountain Journal of Mathematics 17 Acta Mathematica Hungarica 15 Journal d’Analyse Mathématique 15 Aequationes Mathematicae 14 Computational Methods and Function Theory 12 Theoretical Computer Science 11 Bulletin of the Australian Mathematical Society 11 Israel Journal of Mathematics 11 Mathematical Notes 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 The Mathematical Intelligencer 10 Journal of Combinatorial Theory. Series A 10 Monatshefte für Mathematik 10 Linear Algebra and its Applications 9 Discrete & Computational Geometry 8 Mathematische Zeitschrift 8 European Journal of Combinatorics 8 Advances in Applied Mathematics 8 Numerical Algorithms 8 Journal of Mathematical Sciences (New York) 8 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 American Mathematical Monthly 7 Computers & Mathematics with Applications 7 Discrete Mathematics 7 Ukrainian Mathematical Journal 7 BIT 7 Designs, Codes and Cryptography 7 Elemente der Mathematik 7 Journal of the Australian Mathematical Society 6 Discrete Applied Mathematics 6 Lithuanian Mathematical Journal 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Journal of Functional Analysis 6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 6 Indagationes Mathematicae. New Series 5 Analysis Mathematica 5 Journal of Mathematical Physics 5 Acta Arithmetica 5 International Journal of Mathematics and Mathematical Sciences 5 Manuscripta Mathematica 5 Mathematische Annalen 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Numerische Mathematik 5 Results in Mathematics 5 Expositiones Mathematicae 5 St. Petersburg Mathematical Journal 5 Abstract and Applied Analysis 5 Mathematical Inequalities & Applications 5 LMS Journal of Computation and Mathematics 5 Advances in Difference Equations 4 The Mathematical Gazette 4 Periodica Mathematica Hungarica 4 Functiones et Approximatio. Commentarii Mathematici 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Siberian Mathematical Journal 4 The Electronic Journal of Combinatorics 4 Advances in Computational Mathematics 4 Integral Transforms and Special Functions 4 Acta Mathematica Sinica. English Series 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Mediterranean Journal of Mathematics 4 Journal of Mathematical Inequalities 4 Journal of Classical Analysis 4 Open Mathematics 3 Applicable Analysis 3 Indian Journal of Pure & Applied Mathematics 3 Letters in Mathematical Physics 3 Colloquium Mathematicum 3 Journal of Optimization Theory and Applications 3 Mathematika 3 Nagoya Mathematical Journal 3 Acta Applicandae Mathematicae 3 Journal of Symbolic Computation 3 Journal of Complexity 3 The Annals of Applied Probability 3 International Journal of Computer Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 Applied and Computational Harmonic Analysis 3 Journal of Difference Equations and Applications 3 Journal of Integer Sequences 3 Annals of Mathematics. Second Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of High Energy Physics 3 Proceedings of the Steklov Institute of Mathematics 3 Applicable Analysis and Discrete Mathematics ...and 226 more Serials
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### Cited in 59 Fields

 618 Number theory (11-XX) 321 Special functions (33-XX) 271 Approximations and expansions (41-XX) 216 Functions of a complex variable (30-XX) 204 Real functions (26-XX) 135 Numerical analysis (65-XX) 120 Combinatorics (05-XX) 108 Harmonic analysis on Euclidean spaces (42-XX) 75 Computer science (68-XX) 43 Probability theory and stochastic processes (60-XX) 41 Sequences, series, summability (40-XX) 41 Convex and discrete geometry (52-XX) 39 Information and communication theory, circuits (94-XX) 37 Difference and functional equations (39-XX) 36 Dynamical systems and ergodic theory (37-XX) 34 Linear and multilinear algebra; matrix theory (15-XX) 33 Field theory and polynomials (12-XX) 31 Algebraic geometry (14-XX) 30 Operator theory (47-XX) 28 Functional analysis (46-XX) 26 Ordinary differential equations (34-XX) 21 Measure and integration (28-XX) 21 Partial differential equations (35-XX) 21 Geometry (51-XX) 17 Potential theory (31-XX) 17 Statistics (62-XX) 17 Quantum theory (81-XX) 14 History and biography (01-XX) 14 Statistical mechanics, structure of matter (82-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Operations research, mathematical programming (90-XX) 11 Systems theory; control (93-XX) 10 General and overarching topics; collections (00-XX) 10 Group theory and generalizations (20-XX) 9 Topological groups, Lie groups (22-XX) 9 Integral transforms, operational calculus (44-XX) 9 Integral equations (45-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Mathematical logic and foundations (03-XX) 7 Commutative algebra (13-XX) 7 Abstract harmonic analysis (43-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 General topology (54-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 3 Biology and other natural sciences (92-XX) 3 Mathematics education (97-XX) 2 Associative rings and algebras (16-XX) 2 $$K$$-theory (19-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Relativity and gravitational theory (83-XX) 1 General algebraic systems (08-XX) 1 Nonassociative rings and algebras (17-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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