Chris Smyth's minimalist home page.

Algebra Spring 2013

Number Theory Autumn 2012

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

Bhavin Moriya and Chris Smyth, Index-dependent divisors of coefficients of modular forms, submitted.

Jonathan Cooley, James McKee, Chris Smyth, Non-bipartite graphs of small Mahler measure, J. Combinatorics and Number Theory (to appear).

2013:

Matilde Lalín, Chris Smyth, Unimodularity of zeros of self-inversive polynomials, Acta Math. Hungar. 138 (1–2) (2013), 85–101.

James McKee, Chris Smyth, Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros, Cent. Eur. J. Math., 2013, 11(5), 882-899. DOI: 10.2478/s11533-013-0209-9

2012:

James McKee, Chris Smyth, Salem numbers and Pisot numbers via interlacing, Canad. J. Math. 64 (2012), 345--367.

James McKee, Chris Smyth, Integer symmetric matrices of small spectral radius and small Mahler measure, Int. Math. Res. Not. IMRN 2012, no. 1, 102–136, on archive.

Iskander Aliev, Chris Smyth, Solving algebraic equations in roots of unity, Forum Mathematicum, 24 (2012), no. 3, 641--655. DOI: 10.1515/FORM.2011.087

Paulius Drungilas, Arturas Dubickas, Chris Smyth, A degree problem for two algebraic numbers and their sum, Publ. Mat. 56 (2012), 413--448.

2011:

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.

2010:

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.

I Aliev and C J Smyth, Finding maximal torsion cosets on varieties. Proceedings of Conference on Algorithmic Number Theory, May 8-11 2007, Turku, Finland. Turku Centre for Computer Science General Publication, No. 46, 153--164, December 2007.

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)