Publications of Graham Everest
Books
'Heights of Polynomials and Entropy in Algebraic Dynamics' (with Tom Ward), Springer-Verlag, 1999
'Recurrence Sequences' (with Alf van der Poorten, Igor Shparlinski and Tom Ward), AMS Surveys and Monographs, 2003
'An Introduction to Number Theory' (with Tom Ward), Springer Lecture Notes in Mathematics, 2005
Pre-prints
· 'Dirichlet series for finite combinatorial rank dynamics', (with Richard Miles, Shaun Stevens and Tom Ward), Trans. AMS, to appear.
· 'Dual Rectangles', (with Jonny Griffiths), Mathematical Spectrum, to appear.
Published Papers (1996-present)
· 'The Continuing Story of Zeta', (with Christian Roettger and Tom Ward ), Mathematical Intelligencer, 31 no. 3 (2009), 13--17. preprint
· 'A generalization of Siegel's Theorem and Hall's Conjecture', (with Valery Mahe), Experimental Math., 18 (2009), 1--9. preprint
· 'Primitive divisors on twists of the Fermat cubic', (with Patrick Ingram and Shaun Stevens), LMS Journal of Computation and Mathematics, 12 (2009), 54--81. preprint
· 'Descent on elliptic curves and Hilbert's tenth problem' (with Kirsten Eisentraeger), Proceedings of the AMS, 137 (2009), 1951--1959. preprint
· 'The uniform primality conjecture for elliptic curves', (with Patrick Ingram, Valery Mahe and Shaun Stevens), Acta Arithmetica 134 (2008), 157--181. preprint
· 'Primitive divisors of n^2+b', (with Glyn Harman), Number Theory and Polynomials (Conference Proceedings University of Bristol), 142--154, London Mathematical Society Lecture Note Series Vol 352, CUP, Cambridge, 2008. preprint
· 'On the denominators of rational points on elliptic curves', (with Jonathan Reynolds and Shaun Stevens), Bull. London Math. Soc. 39 (5) (2007), 762--770. preprint
· 'Orbit-counting in non-hyperbolic dynamical systems', (with Richard Miles, Shaun Stevens, and Tom Ward) J. Reine Angew. Math. 608 (2007), 155--182. preprint
· 'Primes generated by recurrence sequences' (with Shaun Stevens, Duncan Tamsett and Tom Ward), American Math Monthly, 114 (2007), 417--431. preprint
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· 'Prime powers in elliptic divisibility sequences' (with Helen King), Math. Comp. 74 (2005), 2061-2071. preprint
· 'On some arithmetical properties of solutions of decomposable form equations' (with Kalman Gyory), Math. Proc. Camb. Phil. Soc. 139 (2005), 27-40. preprint
· 'Prime divisors of sequences associated to elliptic curves' (with Igor Shparlinski), Glasgow J. Math. 47 no1 (2005), 115-122 preprint
· 'Periodic points for good reduction maps on curves' (with Manfred Einsiedler, Tom Ward), Geometrica Dedicata, 106 (2004), 29-41. preprint
· 'Primes generated by elliptic curves'(with Victor Miller, Nelson Stephens), Proc. AMS, 132 (2004), 955-963. pre-print
· 'Morphic heights and periodic points'(with Manfred Einsiedler, Tom Ward), New York Number Theory Seminars, (Eds. D Chudnovsky, G Chudnovsky, M Nathanson, Springer-Verlag, 2004. pre-print
· 'Integer sequences and periodic points' (with Alf van der Poorten, Yash Puri, Tom Ward), Journal of Integer Sequences (electronic) 5 (2002), 02.2.3, 1-10.
· 'A higher rank Mersenne problem', (with Peter Rogers, Tom Ward) ANTS V Proceedings, Springer Lecture Notes in Computer Science 2369 (2002), 95-107. preprint.
· 'On the spatial distribution of solutions of decomposable form equations' (with Gaal, Gyory, Rottger), Math. Comp. 71 (2002), 633-648. A ps version of the pre-print is available here .
· 'Entropy and the canonical height' (with Ward, Einsiedler), J. Number Theory 91 (2001), 256-273. Click here for a ps version of the pre-print.
· 'Primes in divisibility sequences' (with Ward), Cubo Mathematica Educacional 3 (2001), 245-259. A ps version of the pre-print is available here .
· 'Primes in elliptic divisibility sequences' (with Einsiedler, Ward), LMS Journal of Computation and Mathematics 4 (2001), 1-13. A ps version of the pre-print is available here .
· 'The canonical height of an algebraic point on an elliptic curve' (with Ward), New York J. Math. 6 (2000), 331-342
· 'Dynamical systems arising from elliptc curves' (with D'Ambros, Miles, Ward), Colloquium Mathematicum, 84-85 (2000), 95-107
· 'Primes in sequences associated to polynomials (after Lehmer)' (with Ward, Einsiedler), LMS Journal of Computation and Mathematics, 3 (2000), 125-139. The ps file of an earlier version is available.
· `Explicit local heights', New York J. Math. 5 (1999), 115-120
· `On the elliptic analogue of Jensen's formula', J. London Math. Soc.(2) 59 (1999), 21-36
· `Counting the values taken by algebraic exponential polynomials', (with I. Shparlinski), Proc. AMS 127 (1999), 665-675
· `Bounding the elliptic Mahler measure II', (with C. Pinner), J. London Math. Soc.(1) 58 (1998), 1-8
· `Counting generators of normal integral bases', Amer. J. Math. 120 (1998), 1007-1018
· `A dynamical interpretation of the global canonical height on an elliptic curve' (with T. Ward), J. Experimental Math. 7 (1998), 315-326
· `Integrating on p-adic Lie groups' (with M. du Sautoy), Israel J. Math. 103 (1998), 207-235
· `Measuring the height of a polynomial', Math. Intell. 20 (1998), 9-16
· `S-integral dynamical systems: periodic points' (with V. Chothi, T. Ward), J. reine angew. Math. 489 (1997), 99-132
· `Counting solution of decomposable form equations' (with K. Gyory), Acta Arith. 79 (1997), 173-191
· `Factorisation in the ring of exponential polynomials' (with A. van der Poorten), Proc. AMS 125 (1997), 1293-1298
· `Divisor sums of generalized exponential polynomials' (with I. Shparlinski), Canad. Bull. Math. 39 (1996), 35-46
· `Oriented local entropies for expansive commuting automorphisms' (with V. Chothi, T. Ward), Israel J. Math. 93 (1996), 281-301
· `The elliptic Mahler measure' (with B. ni Fhlathuin), Math. Proc. Ca,mb. Phil. Soc. 120 (1996), 13-25