122 citations
- University of CanterburyNZ4 papers
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6 papers · 1 filter
Functorial orbit counting
Apisit Pakapongpun, Thomas Ward
We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products…
Primitive Divisors of some Lehmer-Pierce Sequences
Anthony Flatters
We study the primitive divisors of the terms of , where for a real quadratic field, and a unit element of its ring of int…
Primitive divisors on twists of the Fermat cubic
Graham Everest, Patrick Ingram, Shaun Stevens
We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u^3+v^3=m, with m cube-free, all the terms beyond the first have a primitive divisor.
The Continuing Story of Zeta
Graham Everest, Christian Roettger, Tom Ward
We show how the Binomial Theorem can be used to continue the Riemann Zeta Function to the left hand half-plane. This method yields the explicit values of the function at non-positi…
Primitive divisors of elliptic divisibility sequences
Graham Everest, Gerard Mclaren, Tom Ward
Silverman proved the analogue of Zsigmondy's Theorem for elliptic divisibility sequences. For elliptic curves in global minimal form, it seems likely this result is true in a unifo…
Prime divisors of sequences associated to elliptic curves
Graham Everest, Igor E Shparlinski
We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large valu…