All the preprints fit to preprint (and no doubt others)

Recent Publications

In accordance with the usual rules of journals, the versions given here are the final preprint versions, and may differ somewhat from the published versions.

• T.G. Berry. A type of hyperelliptic continued fraction. Monatsh. Math. 145, No. 4, 269-283 (2005).
  abstract
  postscript
  pdf
  
• Pedro Berrizbeitia and T.G. Berry. Biquadratic reciprocity and a Lucasian primality test. Math. Comput. 73 (2004) 1559-1564
  abstract
  postscript
  pdf
  
• Pedro Berrizbeitia, T.G. Berry, Juan Tena Ayuso. A generalization of the Proth theorem. Acta Arithmetica 110 (2003) 107-115
  Postscript
  pdf
  
• T.G. Berry and Richard Patterson. Implicitization and parameterization of cubic surfaces. Comp. Aid. Geom. Des. 18 (2001), 723-738.
  Abstract
  Texfile
  postscript
• Pedro Berrizbeitia and T.G. Berry. Generalized strong pseudoprime tests and applications. J. Symb. Comp. 30 (2) 2000, pp151-160.
  Abstract
  (La)Tex file
  postscript
• T. G. Berry. Groebner bases of the ideals of space curves. J. P. Appl. Alg. 148 (2000), pp17-47.
  abstract
  postscript
• T.G. Berry. Continued fractions in hyperelliptic function fields. In J. Buchman, T. Hoholdt, H. Stichtenoth, H. Tapia-Recillas (Eds.) Coding Theory, Cryptography and Related Areas. Proceedings of an International Conference held in Guanajuato, Mexico, April 1998. Springer, 2000. ISBN 3-540-66248-0.
  ps pdf or tex
• Pedro Berrizbeitia; T. G. Berry ;
  Cubic reciprocity and generalised Lucas-Lehmer tests for primality of $A.3^n\pm1$
  Proc. Amer. Math. Soc. 127 (1999), pp. 1923-1925
  Errata:

  1. In the statement of the theorem, it should read $Q_{k+1} = Q_k(Q_k^2-3)$ instead of
     $Q_{k+1} = Q_k^2(Q_k-3)$.
  2. In the proof, replace $Q_{n-1} = (Tr(\tau))^{A.3^{n-1}}$ by $Q_{n-1} = Tr(\tau^{A \cdot 3^{n-1}})$.

  Many thanks to Franz Lemmermermeyer for these corrections.
• T.G. Berry. Construction of linear systems on hyperelliptic curves. J. Symb. Comp. 26 (1998)pp. 315-327.abstract