# Stephen Choi's Publications

### Book

Peter Borwein, Stephen Choi, Brendan Rooney and Andrea Weirathmuller, The Riemann Hypothesis - A Resource for Afficionado and Virtuoso Alike, CMS Books in Mathematics, Springer-Verlag, New York, 2007. (ISBN:978-0-387-72125-5)

### Papers

1. Stephen Choi and Daniel Tarnu, The Order of the Fundamental Solution of   $X^2-DY^2=1$ in $\mbox{$\mathbb{Z}[$}\sqrt{D}\mbox{$]/\langle D \rangle$}$, Integers, to appear (2022). [pdf]

2. Stephen Choi, Peter Cho-Ho Lam and Daniel Tarnu, Gap Principle of Divisibility Sequences of Polynomials, Journal of Number Theory, 223 (2021), 153-167. [pdf]

3. Stephen Choi, Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials II, Journal of Approximation Theory, 254 June (2020) article 105390. [pdf]

4. J.P. Allouche, Stephen Choi, T. Erdélyi, A. Denise and B. Saffari, Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials, Analysis Mathematica, 45, 705–726 (2019)[pdf]

5. Tsz Ho Chan, Stephen Choi and Peter Cho-Ho Lam, Divisibility on the sequence of perfect squares minus one: The gap principle, Journal of Number Theory, 184 (2018), 473-484. [pdf]

6. Peter Borwein, Stephen Choi, Jonas Jankauskas and Ron Ferguson, On Littlewood Polynomials with prescribed number of zeros insider the unit, Journal of Canadian Mathematical Society, 67 (2015), 507-526. [pdf]

7. Stephen Choi and Tamás Erdélyi, On a Problem of Bourgain concerning the Lp Norms of Exponential Sums, Math. Zeit. 279 (2015), Issue 1-2, 577-584. [pdf]

8. Stephen Choi and Tamás Erdélyi, Sums of Monomials with Large Mahler Measure, Journal of Approximation Theory (Askey's 80th birthday special issue), Volume 197, September 2015, 49–61. .[pdf]

9. Stephen Choi and Tamás Erdélyi, On the Average Mahler Measures and Lp Norms on Littlewood Polynomials, Proceedings of the American Mathematical Society, Series B, 279 (2014), no. 1, 105-120. [pdf]

10. Peter Borwein, Stephen Choi and Jonas Jankauskas, Extremal Mahler Measures and Ls Norms in the Class of Polynomials Related to Barker Sequences, Proceedings of Amer. Math. Soc., 141 (2013), no. 8, 2653-2633. [pdf]

11. Peter Borwein, Stephen Choi and Himadri Ganguli, Signs Changes of the Liouville Function on Quadratics, Canad. Math. Bull., 56 (2013), no.2, 251--257. [pdf]

12. Peter Borwein, Stephen Choi, Greg Martin and Charles Samuels, Polynomials whose reducibility is related to the Goldbach Conjecture, Journal of Algebra, Number Theory and Applications, 26 No.1, 33-63 (2012). [pdf]

13. Peter Borwein, Stephen Choi and Jonas Jankauskas, On a Class of Polynomials Related to Barker Sequences, Proceedings of Amer. Math. Soc., 140 (2012) 2613-2656. [pdf]

14. Stephen Choi and Charles Samuels, Two Inequalities on the Areal Mahler Measure, Illinois Journal of Mathematics, 56 (2012), no.3, 825-834. [pdf]

15. Stephen Choi and Micheal Mossinghoff, Average Mahler Measure and Lp Norms of Unimodular Polynomials, Pacific Journal of Mathematics, 252 (2011), no.1, 31--50. [pdf]

16. Tsz Ho Chan, Stephen Choi and Kai Man Tsang, An Extension to the Brun-Titchmarsh Theorem, Quarterly Journal of Mathematics, 62 (2011), no.2, 307--322. [pdf]

17. Peter Borwein, Stephen Choi and Michael Coons, Completely Multiplicative Functions Taking Values in {-1, 1}, Trans. Amer. Math. Soc., 362 (2010) 6279-6291. [pdf]

18. Peter Borwein, Stephen Choi and Idris Mercer, Expected Norms of Zero-One Polynomials, Canad. Math. Bull., 51 (2008), no 4, 497--507. [pdf]

19. Shabnam Akhtari and Stephen Choi, On the Littlewood Cyclotomic Polynomials, J. Number Theory, 128 (2008), no. 4, 884-894. [pdf]

20. Stephen Choi and Ping Zhou, On Linear Independence of a Certain Multivariate Infinite Product, Canad. Math. Bull, 51 (2008), no 1, 32-46. [pdf]

21. Peter Borwein and Stephen Choi, The average norm of polynomials of fixed height, Trans. Amer. Math. Soc., 359 (2007) 923-936. [pdf]

22. Stephen Choi and Angel Kumchev, Mean Values of Dirichlet Polynomials and Applications to Linear Equations with Primes Variables, Acta Arithmetica, 123 (2006), 125-142. [pdf]

23. Peter Borwein, Stephen Choi and Frank Chu, An Old Conjecture of Erdös-Turán on Additive Bases, Mathematics of Computation, 75 (2006) 475-484. [pdf]

24. Stephen Choi, Angel Kumchev and Robert Osburn, On Sums of Three Squares, International Journal of Number Theory, 1 (2005), no.2, 161--173. [pdf]

25. Peter Borwein, Stephen Choi and Ron Ferguson, Norm of Littlewood Cyclotomic Polynomials, Mathematical Proceedings Cambridge Philosophical Society, 138 (2005) 315-326. [pdf]

26. Stephen Choi and Jianya Liu, Small prime solutions of quadratic equations II, Proceedings of the American Mathematical Society, 133 (2005) 945-951. [pdf]

27. Jonathan Borwein, Stephen Choi and Wilfried Pigulla, Continued fractions of tails of hypergeometric series, MAA Monthly, 112 (2005), no.6, 493--501. [pdf]

28. Stephen Choi and Angel Kumchev, Quadratic Equations with Five Prime Unknowns, J. Number Theory, 107 (2004), no. 2, 357--367. [pdf]

29. Jonathan Borwein and Stephen Choi, Dirichlet series for squares of sums of squares: a summary, Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, Volume 36 (2004), 27-34. [pdf]

30. Peter Borwein, Stephen Choi and Jonathan Jedwab, Binary sequences with merit factors greater than 6.34, IEEE Transactions on Information Theory, Vol. 50, (2004) Issue 12, 3234-3249. [pdf]

31. Jonathan Borwein and Stephen Choi, On Dirichlet series for sums of squares, The Ramanujan Journal, special issue for Robert Rankin, 7 (2003) No. 1-3, 97-129. [pdf]

32. Stephen Choi and Jianya Liu, Small prime solutions of quadratic equations, Canad. J. Math., 54 (2002), no 1, 71--91. [pdf]

33. Peter Borwein and Stephen Choi, Explicit merit factor formulae for Fekete and Turyn Polynomials, Trans. Amer. Math. Soc., 354 (2002), 219--234. [pdf]

34. Peter Borwein and Stephen Choi, Merit factors of polynomials formed by Jacobi symbols, Canad. J. Math., 53 (2001), no. 1, 33--50. [pdf]

35. Peter Borwein, Stephen Choi and Soroosh Yazdani, An extremal property of Fekete polynomials, Proc. Amer. Math. Soc., 129 (2001), no. 1, 19--27. [pdf]

36. Peter Borwein and Stephen Choi, Merit factors of character polynomials, J. London Math. Soc. (2) 61 (2000), no. 3, 706--720. [pdf]

37. Daniel Bump, Kwok-Kwong Choi, Pär Kurlberg and Jeffrey Vaaler, A local Riemann hypothesis. I, Math. Zeit., 233 (2000), no. 1,1--19. [pdf]

38. Kwok-Kwong Choi and Man-Keung Siu, Counter-examples to a problem of Cohn on classifying characters, J. Number Theory, 84 (2000), no. 1, 40--48. [pdf]

39. Jonathan Borwein and Stephen Choi, On the representations of xy+yz+zx, Experiment. Math., 9 (2000), no. 1, 153--158. [pdf]

40. Kwok-Kwong Choi, On the distribution of points in projective space of bounded height, Trans. Amer. Math. Soc., 352 (2000), no. 3, 1071--1111. [pdf]

41. Peter Borwein and Stephen Choi, On cyclotomic polynomials with +1 or -1 coefficients, Experiment. Math., 8 (1999), no. 4, 399--407. [pdf]

42. Kwok-Kwong Choi and Jeffrey D. Vaaler, Diophantine approximation in projective space, Number theory (Ottawa, ON, 1996), 55--65, CRM Proc. Lecture Notes, 19, Amer. Math. Soc., Providence, RI, 1999. [pdf]

43. Stephen Choi, A numerical bound for Baker's constant -- some explicit estimates for small prime solutions of linear equations, Bull. Hong Kong Math. Soc., 1 (1997), no. 1, 1--19. [pdf]

44. Kwok-Kwong Choi, Ming Chit Liu and Kai Man Tsang, Small prime solutions of linear equations. II, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Univ. Salerno, Salerno, 1992, 1--16. [pdf]

45. Kwok-Kwong Choi, Ming Chit Liu and Kai Man Tsang, Conditional bounds for small prime solutions of linear equations, Manuscripta Math., 74 (1992), no. 3, 321--340. [pdf]