David Harvey

Senior Lecturer at the School of Mathematics and Statistics, University of New South Wales.

Contact details

email: d DOT harvey AT unsw DOT edu DOT au (PGP public key)
phone: +61 (2) 9385-7088
office: 6108 Red Centre
postal: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia

Research interests

Computational number theory and arithmetic geometry, polynomial and integer arithmetic

Grants and awards

Publications and preprints

(click on the publication title for more details)

  1. Even faster integer multiplication (with Joris van der Hoeven and Grégoire Lecerf).
  2. Faster polynomial multiplication over finite fields (with Joris van der Hoeven and Grégoire Lecerf).
  3. Computing zeta functions of arithmetic schemes.
  4. Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time (with Andrew Sutherland).
  5. An incomplete variant of Wilson's congruence (with Joel Beeren and Tim Trudgian).
  6. Counting points on hyperelliptic curves in average polynomial time, Ann. of Math. (2) 179 (2014), no. 2, 783–803.
  7. A search for Wilson primes (with Edgar Costa and Robert Gerbicz), to appear in Mathematics of Computation.
  8. A subquadratic algorithm for computing the n-th Bernoulli number, Math. Comp. 83 (2014), 2471–2477.
  9. Faster arithmetic for number-theoretic transforms, J. Symb. Comp. 60 (2014) 113–119.
  10. Faster deterministic integer factorization (with Edgar Costa), Math. Comp. 83 (2014), 339–345.
  11. Statistics of different reduction types of Fermat curves (with Igor Shparlinski), Exper. Math. 22 (2013), no. 3, 243–249.
  12. The Karatsuba integer middle product, J. Symb. Comp. 47 (2012), 954–967.
  13. Fast computation of Bernoulli, Tangent and Secant numbers (with Richard Brent), Springer Proceedings in Mathematics & Statistics, Vol. 50, 2013, 127–142.
  14. Short division of long integers (with Paul Zimmermann), proceedings of ARITH 20, 2011, 7–14.
  15. Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces (with Brendan Hassett and Yuri Tschinkel), Comm. Pure Appl. Math. 65 (2012), no. 2, 264–286.
  16. An in-place truncated Fourier transform and applications to polynomial multiplication (with Daniel Roche), proceedings of ISSAC 2010, 325–329.
  17. Irregular primes to 163 million (with Joe Buhler), Math. Comp. 80 (2011), 2435–2444.
  18. Faster exponentials of power series.
  19. Faster algorithms for the square root and reciprocal of power series, Math. Comp. 80 (2011), 387–394.
  20. A multimodular algorithm for computing Bernoulli numbers, Math. Comp. 79 (2010), 2361–2370.
  21. Faster polynomial multiplication via multipoint Kronecker substitution, J. Symb. Comp. 44 (2009), 1502–1510.
  22. A cache-friendly truncated FFT, Theor. Comput. Sci. 410 (2009), 2649–2658.
  23. Algorithms for p-adic cohomology and p-adic heights, Ph.D. thesis.
  24. Efficient computation of p-adic heights, LMS J. Comput. Math. 11 (2008), 40–59.
  25. Kedlaya's algorithm in larger characteristic, Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29.
  26. Selberg's symmetry formula, Expo. Math. 22 (2004), no. 2, 185–195.