| David Harvey |
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Faster enumeration of primes
D. Harvey |
• arXiv preprint |
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The accumulating remainder tree and its impact in number theory
D. Harvey Proceedings of 2026 ICM |
• published version (DOI) |
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Deterministic methods for finding elements of large multiplicative order
D. Harvey and M. Hittmeir Submitted for publication |
• arXiv preprint |
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Integer multiplication is at least as hard as matrix transposition
D. Harvey and J. van der Hoeven Presented at FOCS 2025 |
• arXiv preprint • HAL preprint |
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Faster truncated integer multiplication
D. Harvey Math. Comp. 93 (2024), 1265–1296 |
• published version (DOI) • arXiv preprint • demo code |
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Counting points on smooth plane quartics
E. Costa, D. Harvey and A. V. Sutherland Proceedings of ANTS XV, Res. Number Theory 9 (2023), no.1, Paper No. 1 |
• published version (DOI) • arXiv preprint |
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A deterministic algorithm for finding r-power divisors
D. Harvey and M. Hittmeir Proceedings of ANTS XV, Res. Number Theory 8 (2022), no.4, Paper No. 94 |
• published version (DOI) • arXiv preprint |
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A log-log speedup for exponent one-fifth deterministic integer factorisation
D. Harvey and M. Hittmeir Math. Comp. 91 (2022), 1367–1379 |
• published version (DOI) • arXiv preprint |
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Polynomial multiplication over finite fields in time O(n log n)
D. Harvey and J. van der Hoeven J. ACM 69 (2022), no. 2, Article 12 |
• published version (DOI) • HAL preprint |
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An exponent one-fifth algorithm for deterministic integer factorisation
D. Harvey Math. Comp. 90 (2021), 2937–2950 |
• published version (DOI) • arXiv preprint |
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Integer multiplication in time O(n log n)
D. Harvey and J. van der Hoeven Ann. of Math. (2) 193 (2021), no. 2, 563–617 |
• published version (DOI) • HAL preprint • media coverage and FAQ |
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Faster integer and polynomial multiplication using cyclotomic coefficient rings
D. Harvey and J. van der Hoeven The integer multiplication algorithm in this paper will remain unpublished (it was superseded by subsequent work). The polynomial multiplication algorithm can be found in the paper Faster polynomial multiplication over finite fields using cyclotomic coefficient rings. |
• arXiv preprint |
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Faster polynomial multiplication over finite fields using cyclotomic coefficient rings
D. Harvey and J. van der Hoeven J. Complexity 54 (2019), 101404 |
• published version (DOI) |
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Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology
E. Costa, D. Harvey and K. S. Kedlaya Proceedings of ANTS 13, Open Book Series Vol 2 (2019), 221–238 |
• published version (DOI) • arXiv preprint |
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Faster integer multiplication using short lattice vectors
D. Harvey and J. van der Hoeven Proceedings of ANTS 13, Open Book Series Vol 2 (2019), 293–310 |
• published version (DOI) • arXiv preprint |
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Faster integer multiplication using plain vanilla FFT primes
D. Harvey and J. van der Hoeven Math. Comp. 88 (2019), 501–514 |
• published version (DOI) • arXiv preprint |
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On the complexity of integer matrix multiplication
D. Harvey and J. van der Hoeven J. Symb. Comp. 89 (2018) 1–8 |
• published version (DOI) • HAL preprint |
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Irregular primes to two billion
W. Hart, D. Harvey and W. Ong Math. Comp. 86 (2017), 3031–3049 |
• published version (DOI) • arXiv preprint • list of irregular pairs (557 MB) |
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Faster polynomial multiplication over finite fields
D. Harvey, J. van der Hoeven and G. Lecerf J. ACM 63 (2017), no. 6, Article 52 The preprint version includes some extra material on a conjectural algorithm that improves the 8 to 4, but this did not make it into the published version. |
• published version (DOI) • arXiv preprint • HAL preprint |
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Computing L-series of geometrically hyperelliptic curves of genus three
D. Harvey, M. Massierer and A. V. Sutherland LMS J. Comput. Math. 19 (2016), suppl. A, 220–234 (Proceedings of ANTS 12) |
• published version (DOI) • arXiv preprint |
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Fast polynomial multiplication over F260
D. Harvey, J. van der Hoeven and G. Lecerf Proceedings of ISSAC 2016, 255–262 |
• published version (DOI) • HAL preprint |
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Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II
D. Harvey and A. V. Sutherland Contemporary Mathematics 663 (2016), “Frobenius distributions: Lang–Trotter and Sato–Tate conjectures”, 127–147, AMS |
• published version (DOI) • arXiv preprint |
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Even faster integer multiplication
D. Harvey, J. van der Hoeven and G. Lecerf J. Complexity 36 (2016), 1–30 Winner of 2016 Journal of Complexity Best Paper Award |
• published version (DOI) • arXiv preprint • HAL preprint |
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Computing zeta functions of arithmetic schemes
D. Harvey Proc. Lond. Math. Soc. 111 (2015), no. 6, 1379–1401 |
• published version (DOI) • arXiv preprint |
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Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
D. Harvey and A. V. Sutherland LMS J. Comput. Math. 17 (2014), Special Issue A, 257–273 (Proceedings of ANTS 11) |
• published version (DOI) • arXiv preprint • erratum |
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Counting points on hyperelliptic curves in average polynomial time
D. Harvey Ann. of Math. (2) 179 (2014), no. 2, 783–803 |
• published version (DOI) • arXiv preprint |
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A search for Wilson primes
E. Costa, R. Gerbicz and D. Harvey Math. Comp. 83 (2014), 3071–3091 |
• published version (DOI) • arXiv preprint • list of Wilson quotients (247 MB) |
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A subquadratic algorithm for computing the n-th Bernoulli number
D. Harvey Math. Comp. 83 (2014), 2471–2477 |
• published version (DOI) • arXiv preprint |
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Faster arithmetic for number-theoretic transforms
D. Harvey J. Symb. Comp. 60 (2014) 113–119 |
• published version (DOI) • arXiv preprint • demo code |
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Faster deterministic integer factorization
E. Costa and D. Harvey Math. Comp. 83 (2014), 339–345 |
• published version (DOI) • arXiv preprint |
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Statistics of different reduction types of Fermat curves
D. Harvey and I. Shparlinski Exper. Math. 22 (2013), no. 3, 243–249 |
• published version (DOI) • arXiv preprint |
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The Karatsuba integer middle product
D. Harvey J. Symb. Comp. 47 (2012), 954–967 The published version is substantially revised and improved compared to the preprint version. |
• published version (DOI) • preprint • code |
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Fast computation of Bernoulli, Tangent and Secant numbers
R. P. Brent and D. Harvey Computational and Analytical Mathematics, Springer Proceedings in Mathematics & Statistics, Vol. 50, 2013, 127–142 |
• published version (DOI) • arXiv preprint |
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Short division of long integers
D. Harvey and P. Zimmermann Proceedings of ARITH 20, Tuebingen, July 25-27, 2011, 7–14 |
• published version (DOI) • preprint |
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Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces
D. Harvey, B. Hassett and Y. Tschinkel Comm. Pure Appl. Math. 65 (2012), no. 2, 264–286 |
• published version (DOI) • arXiv preprint |
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An in-place truncated Fourier transform and applications to polynomial multiplication
D. Harvey and D. Roche Proceedings of ISSAC 2010, Munich, 325–329 |
• published version (DOI) • arXiv preprint |
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Irregular primes to 163 million
J. Buhler and D. Harvey Math. Comp. 80 (2011), 2435–2444 The data files associated with this paper have been superseded by the followup paper Irregular primes to two billion. Please contact me for access to the original files. |
• published version (DOI) • arXiv preprint |
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Faster exponentials of power series
D. Harvey |
• arXiv preprint |
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Faster algorithms for the square root and reciprocal of power series
D. Harvey Math. Comp. 80 (2011), 387–394 |
• published version (DOI) • arXiv preprint |
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A multimodular algorithm for computing Bernoulli numbers
D. Harvey Math. Comp. 79 (2010), 2361–2370 |
• published version (DOI) • arXiv preprint • data files |
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Faster polynomial multiplication via multipoint Kronecker substitution
D. Harvey J. Symb. Comp. 44 (2009), 1502–1510 An implementation of the algorithm can be found in the file mul_ks.c in the zn_poly package. |
• published version (DOI) • arXiv preprint |
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A cache-friendly truncated FFT
D. Harvey Theor. Comput. Sci. 410 (2009), 2649–2658 |
• published version (DOI) • arXiv preprint |
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Algorithms for p-adic cohomology and p-adic heights
D. Harvey Ph.D. thesis (2008) This thesis has essentially the same content as the papers Kedlaya's algorithm in larger characterstic and Efficient computation of p-adic heights, plus some algorithmic improvements. |
• final version |
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Efficient computation of p-adic heights
D. Harvey LMS J. Comput. Math. 11 (2008), 40–59 |
• published version (DOI) • arXiv preprint |
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Kedlaya's algorithm in larger characteristic
D. Harvey Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29 |
• published version (DOI) • arXiv preprint |
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Selberg's symmetry formula
D. Harvey Expo. Math. 22 (2004), no. 2, 185–195 |
• published version (DOI) |