Chris Smyth's minimalist home page.

Misc

Ramanujan's tau function τ(n) for n up to 1,000,000

James Cook Mathematical Notes

Four herons in Regent's Park, London, 25 March 2005 (photo: Dan Salter)

Family photos: you have been warned!

Recent preprints and papers

James McKee, Chris Smyth, Pairs of cyclotomic polynomials with interlacing roots, submitted.

Matilde Lalín, Chris Smyth, Unimodularity of zeros of self-inversive polynomials, Acta Math. Hungarica (to appear).

Jonathan Cooley, James McKee, Chris Smyth, Non-bipartite graphs of small Mahler measure, submitted.

Paulius Drungilas, Arturas Dubickas, Chris Smyth, A degree problem for two algebraic numbers and their sum, Publicacions Matemàtiques (to appear).

2011:

James McKee, Chris Smyth, Salem numbers and Pisot numbers via interlacing, Canad. J. Math. Published online 2011-08-03: published version (journal subscription required)

Karl Dilcher, Rob Noble, Chris Smyth, Minimal polynomials of algebraic numbers with rational parameters, Acta Arith. 148 (2011), no. 3, 281--308. Slides

Ram Murty, Chris Smyth, Rob Wang Zeros of Ramanujan polynomials, J. Ramanujan Math. Soc. 26 (2011), no. 1, 107--125.

James McKee, Chris Smyth: Integer symmetric matrices of small spectral radius and small Mahler measure, International Mathematics Research Notices 2011; published online doi: 10.1093/imrn/rnr011 or on archive.

2010:

Iskander Aliev, Chris Smyth, Solving algebraic equations in roots of unity, Forum Mathematicum, published online 01/12/2010, DOI: 10.1515/FORM.2011.087

Kalman Gyory, Chris Smyth, The divisibility of a^n - b^n by powers of n Integers 10(2010), 319-334.

Chris Smyth, The terms in Lucas sequences divisible by their indices, J. Integer Seq. 13(2010), No. 2, Article ID 10.2.4, 18 pp.

Jan Hilmar, Chris Smyth, Euclid meets Bezout: Intersecting algebraic plane curves with the Euclidean algorithm, Amer. Math. Monthly 117 (2010), no. 3, 250-260.

2008:

C J Smyth, Mahler measure of one-variable polynomials: a survey. Conference proceedings, University of Bristol, 3-7 April 2006, LMS Lecture Note Series 352, Cambridge University Press, Cambridge, 2008, pp. 322-349.

A Dubickas and C J Smyth, On the lines passing through two conjugates of a Salem number. Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 29--37.

2007:

J F McKee and C J Smyth, Integer symmetric matrices having all their eigenvalues in the interval [-2,2]. J. Algebra 317 (2007), no. 1, 260--290.

2006:

K G Hare and C J Smyth, The monic integer transfinite diameter, Math. Comp. 75(2006), 1997--2019 (as corrected in Math. Comp. 77 (2008), no. 263, 1869.)

2005:

J F McKee and C J Smyth, There are Salem numbers of every trace, Bull. LMS 37(2005), 25-36.

A Dubickas and C J Smyth, Length of the sum and product of algebraic numbers, Math. Notes 77(2005), 787-793(with A. Dubickas).

J F McKee and C J Smyth, Salem numbers, Pisot numbers, Mahler measure and graphs, Exper. Math. 14(2005), 211-229.

A Dubickas and C J Smyth, Two variations of a theorem of Kronecker, Expos. Math. 23(2005) 289--294.

2004:

N. Berry, A. Dubickas, N.Elkies, B. Poonen and C J Smyth, The conjugate dimension of algebraic numbers Quart. J. Math. 55(2004), 237-252.

J F McKee and C J Smyth, Salem numbers of trace -2 and traces of totally positive algebraic integers. Proceedings of 6th Algorithmic Number Theory Symposium (University of Vermont 13 - 18 June 2004), Springer Lecture Notes in Computer Science 3076(2004) (D. Buell, Editor) 327-337.

2003:

A Dubickas and C J Smyth, On metric heights, Periodica Math. Hung. 46 (2)(2003), 135-155.

C J Smyth, Explicit formulas for the Mahler measure of families of multivariable polynomials, preprint (not so recent).

2002:

F Beukers and C J Smyth, Cyclotomic points on curves. In: Number Theory for the Millenium I, A.K. Peters 2002 ( Proceedings of the Millennial Conference on number theory, Urbana May 21-26 2000), 67-85.

C J Smyth, An explicit formula for the Mahler measure of a family of 3-variable polynomials. J. Theor. Nombres Bordeaux 14 (2002), 683-700.

A Dubickas and C J Smyth, Variations on the theme of Hilbert's Theorem 90. Glasgow Math. J. 22 (2002), 435-441.
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Chris Smyth (c.smyth"AT"ed.ac.uk)