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- Nils Bruin, Kevin Doerksen
- 2009

In this paper we study genus 2 curves whose Jacobians are (4, 4)-isogenous to a product of elliptic curves. Such Jacobians are called (4, 4)-split. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We give a generic model such that any genus 2 curve with optimally (4, 4)-split Jacobian can… (More)

Let (bn) = (b1, b2, . . . ) be a sequence of integers. A primitive prime divisor of a term bk is a prime which divides bk but does not divide any of the previous terms of the sequence. A zero orbit of a polynomial φ(z) is a sequence of integers (cn) where the n-th term is the n-th iterate of φ at 0. We consider primitive prime divisors of zero orbits of… (More)

- Kevin Doerksen
- ACM Comm. Computer Algebra
- 2008

of Φn(z), respectively. The aim of our research is to study An and Sn. In particular, we are looking for cyclotomic polynomials with large heights. We present two algorithms to calculate cyclotomic polynomials. Our first algorithm uses that for primes p n, Φnp(z) = Φn(z) ÷ Φn(z). We perform fast polynomial division via the discrete fast Fourier transform.… (More)

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