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


Publications and preprints

(click on the publication title for more details)

  1. Faster truncated integer multiplication
  2. Faster integer multiplication using plain vanilla FFT primes (with Joris van der Hoeven)
  3. Computing L-series of geometrically hyperelliptic curves of genus three (with Maike Massierer and Andrew Sutherland)
    To appear in proceedings of ANTS XII.
  4. Irregular primes to two billion (with William Hart and Wilson Ong)
    To appear in Mathematics of Computation.
  5. On the complexity of integer matrix multiplication (with Joris van der Hoeven)
    To appear in the Journal of Symbolic Computation.
  6. Faster polynomial multiplication over finite fields (with Joris van der Hoeven and Grégoire Lecerf)
    J. ACM 63 (2017), no. 6, Article 52
  7. Fast polynomial multiplication over F_(2^60) (with Joris van der Hoeven and Grégoire Lecerf)
    To appear in proceedings of ISSAC 2016.
  8. Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II (with Andrew Sutherland)
    Contemporary Mathematics 663 (2016), “Frobenius distributions: Lang–Trotter and Sato–Tate conjectures”, 127–147, AMS.
  9. Even faster integer multiplication (with Joris van der Hoeven and Grégoire Lecerf)
    J. Complexity 36 (2016), 1–30.
  10. Computing zeta functions of arithmetic schemes
    Proc. Lond. Math. Soc. 111 (2015), no. 6, 1379–1401.
  11. Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time (with Andrew Sutherland)
    LMS J. Comput. Math. 17 (2014), Special Issue A, 257–273.
  12. Counting points on hyperelliptic curves in average polynomial time
    Ann. of Math. (2) 179 (2014), no. 2, 783–803.
  13. A search for Wilson primes (with Edgar Costa and Robert Gerbicz)
    Math. Comp. 83 (2014), 3071–3091.
  14. A subquadratic algorithm for computing the n-th Bernoulli number
    Math. Comp. 83 (2014), 2471–2477.
  15. Faster arithmetic for number-theoretic transforms
    J. Symb. Comp. 60 (2014) 113–119.
  16. Faster deterministic integer factorization (with Edgar Costa)
    Math. Comp. 83 (2014), 339–345.
  17. Statistics of different reduction types of Fermat curves (with Igor Shparlinski)
    Exper. Math. 22 (2013), no. 3, 243–249.
  18. The Karatsuba integer middle product
    J. Symb. Comp. 47 (2012), 954–967.
  19. Fast computation of Bernoulli, Tangent and Secant numbers (with Richard Brent)
    Springer Proceedings in Mathematics & Statistics, Vol. 50, 2013, 127–142.
  20. Short division of long integers (with Paul Zimmermann)
    Proceedings of ARITH 20, 2011, 7–14.
  21. 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.
  22. An in-place truncated Fourier transform and applications to polynomial multiplication (with Daniel Roche)
    Proceedings of ISSAC 2010, 325–329.
  23. Irregular primes to 163 million (with Joe Buhler)
    Math. Comp. 80 (2011), 2435–2444.
  24. Faster exponentials of power series
  25. Faster algorithms for the square root and reciprocal of power series
    Math. Comp. 80 (2011), 387–394.
  26. A multimodular algorithm for computing Bernoulli numbers
    Math. Comp. 79 (2010), 2361–2370.
  27. Faster polynomial multiplication via multipoint Kronecker substitution
    J. Symb. Comp. 44 (2009), 1502–1510.
  28. A cache-friendly truncated FFT
    Theor. Comput. Sci. 410 (2009), 2649–2658.
  29. Algorithms for p-adic cohomology and p-adic heights
    Ph.D. thesis.
  30. Efficient computation of p-adic heights
    LMS J. Comput. Math. 11 (2008), 40–59.
  31. Kedlaya's algorithm in larger characteristic
    Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29.
  32. Selberg's symmetry formula
    Expo. Math. 22 (2004), no. 2, 185–195.




Not currently teaching any courses.

Please contact me if you are interested in doing an Honours project or postgraduate work in number theory, computational number theory, etc.

Current and past students:

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