Dr Keith Matthews
Honorary Senior Fellow
School of Mathematics and Physics
+61 7 336 53277
Personal Page
Book Chapter
Matthews, Keith R. (2010). Generalized 3x+1 mappings: Markov chains and ergodic theory. The ultimate challenge: The 3x+1 problem. (pp. 79-103) edited by Jeffrey C. Lagarias. Providence, RI, U.S.A.: American Mathematical Society.
Journal Articles
Matthews, Keith R. and Robertson, John P. (2021). On solving a binary quadratic Diophantine equation. Rocky Mountain Journal of Mathematics, 51 (4), 1369-1385. doi: 10.1216/rmj.2021.51.1369
Matthews, Keith R. , Robertson, John P. and Srinivasan, Anitha (2017). Extending Theorems of Serret and Pavone. Journal of Integer Sequences, 20 (10) 17.10.5, 1-11.
Matthews, Keith R., Robertson, John P. and Srinivasan, Anitha (2015). On fundamental solutions of binary quadratic form equations. Acta Arithmetica, 169 (3), 291-299. doi: 10.4064/aa169-3-4
Matthews, Keith R. (2014). Lagrange's Algorithm Revisited: Solving at2 + btu + cu2 = n in the case of negative discriminant. Journal of Integer Sequences, 17 (11).
Matthews, Keith R., Robertson, John P. and White, Jim (2013). On a diophantine equation of Andrej Dujella. Glasnik Matematicki, 48 (2), 265-289. doi: 10.3336/gm.48.2.04
Matthews, Keith R. (2012). On the optimal continued fraction expansion of a quadratic surd. Journal of the Australian Mathematical Society, 93 (1-2), 133-156. doi: 10.1017/S1446788712000596
Matthews, Keith R. and Robertson, John P. (2011). Period-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd. Glasnik Matematicki, 46 (2), 269-282. doi: 10.3336/gm.46.2.01
Matthews, Keith R. and Robertson, John P. (2010). Purely periodic nearest square continued fractions. Journal of Combinatorics and Number Theory, 2 (3), 239-244.
Matthews, Keith, Robertson, John and White, Jim (2010). Midpoint criteria for solving Pell's equation using the nearest square continued fraction. Mathematics of Computation, 79 (269), 485-499. doi: 10.1090/S0025-5718-09-02286-8
Matthews, Keith R. (2009). Unisequences and nearest integer continued fraction midpoint criteria for Pell’s equation. Journal of Integer Sequences, 12 (6), Article 09.6.7.
Robertson, John P. and Matthews, Keith R. (2008). A continued fractions approach to a result of Feit. American Mathematical Monthly, 115 (4), 346-349. doi: 10.1080/00029890.2008.11920534
Matthews, Keith R., Robertson, John P. and White, Jim (2008). Corrigenda to “Calculation of the regulator of Q(√D) by use of the nearest integer continued fraction algorithm”. Mathematics of Computation, 78 (265), 615-616. doi: 10.1090/S0025-5718-08-02142-X
Jackson, Terrence and Matthews, Keith (2002). On Shanks' algorithm for computing the continued fraction of log b a. Journal of Integer Sequences, 5 (2.7), 1-9.
Matthews, K. (2002). Thue's theorem and the diophantine equation x2 - Dy2 = ±N. Mathematics of Computation, 71 (239), 1281-1286. doi: 10.1090/S0025-5718-01-01381-3
Matthews, K. (2002). The Diophantine equation ax2 + bxy + cy2 = N, D = b2 - 4ac > 0. Journal de Theorie des Nombres, 14 (1), 257-270. doi: 10.5802/jtnb.358
Matthews, K. R. (2000). The diophantine equation x2 - Dy2 = N, D > 0. Expositiones Mathematicae, 18, 323-331.
Havas, George, Majewski, Bohdan S. and Matthews, Keith R. (1999). Extended GCD and hermite normal form algorithms via lattice basis reduction (Addenda and errata). Experimental Mathematics, 8 (2), 205-205. doi: 10.1080/10586458.1999.10504399
Havas, George, Majewski, Bohdan S. and Matthews, Keith R. (1998). Extended GCD and hermite normal form algorithms via lattice basis reduction. Experimental Mathematics, 7 (2), 125-136. doi: 10.1080/10586458.1998.10504362
Matthews K.R. (1996). Minimal multipliers for consecutive Fibonacci numbers. Acta Arithmetica, 75 (3), 205-218. doi: 10.4064/aa-75-3-205-218
Matthews, Keith R. (1992). A rational canonical form algorithm. Mathematica Bohemica, 117 (3), 315-324. doi: 10.21136/mb.1992.126286
Matthews, K. (1992). Some Borel measures associated with the generalized Collatz mapping. Colloquium Mathematicum, 63 (2), 191-202. doi: 10.4064/cm-63-2-191-202
Buttsworth, R. and Matthews, K. (1990). On some Markov matrices arising from the generalized Collatz mapping. Acta Arithmetica, 55 (1), 43-57. doi: 10.4064/aa-55-1-43-57
Matthews, Keith (1988). Algorithm of the Bi_Month: Computing mth Roots. The College Mathematics Journal, 19 (2), 174. doi: 10.2307/2686184
Matthews, K.R and Leigh, G.M (1987). A generalization of the Syracuse algorithm in Fq[x]. Journal of Number Theory, 25 (3), 274-278. doi: 10.1016/0022-314X(87)90032-1
Matthews, K. and Watts, A. (1985). A markov approach to the generalized Syracuse algorithm. Acta Arithmetica, 45 (1), 29-42. doi: 10.4064/aa-45-1-29-42
Matthews, K. R. (1978). On the eulericity of a graph. Journal of Graph Theory, 2 (2), 143-148. doi: 10.1002/jgt.3190020207
Matthews K.R. (1977). An example from power residues of the critical problem of Crapo and Rota. Journal of Number Theory, 9 (2), 203-208. doi: 10.1016/0022-314X(77)90023-3
Matthews, K. (1976). A generalisation of Artin's conjecture for primitive roots. Acta Arithmetica, 29 (2), 113-146. doi: 10.4064/aa-29-2-113-146
Matthews, K. R. (1973). Hermitian forms and the large and small sieves. Journal of Number Theory, 5 (1), 16-23. doi: 10.1016/0022-314X(73)90054-1
Matthews, K. R. (1972). Bilinear form associated with large sieve. Journal of the London Mathematical Society-Second Series, 5 (OCT), 567-+.
Matthews, K. R. (1972). Inequality of Davenport and Halberstam. Journal of the London Mathematical Society-Second Series, 4 (MAY), 638-+.
Matthews K.R. and Walters R.F.C. (1970). Some properties of the continued fraction expansion of (m/n) e1/q. Mathematical Proceedings of the Cambridge Philosophical Society, 67 (1), 67-74. doi: 10.1017/S0305004100057108
Matthews, K. R. (1965). Polynomials which are near to k-th powers. Mathematical Proceedings of the Cambridge Philosophical Society, 61 (1), 1-5. doi: 10.1017/s0305004100038561
Theses
Matthews, Keith Robert (1974). An investigation of the Davenport-Halberstam inequality and a generalization of Artin's conjecture for primitive roots. PhD Thesis, School of Mathematics and Physics, The University of Queensland.
Matthews, Keith Robert. (1966). Waring's theorem for polynomials over a finite field. M.Sc Thesis, School of Physical Sciences, The University of Queensland.