By Associate Professor David Harvey

Book Chapters

Brent RP; Harvey D, 2013, 'Fast Computation of Bernoulli, Tangent and Secant Numbers', in Baile DHB; Bauschke HH; Borwein P; Garvan F; Théra M; Vanderwerff JD; Wolkowicz H (ed.), Computational and Analytical Mathematics, pp. 127 - 142, http://dx.doi.org/10.1007/978-1-4614-7621-4_8

Journal articles

Harvey D, 2024, 'FASTER TRUNCATED INTEGER MULTIPLICATION', Mathematics of Computation, 93, pp. 1265 - 1296, http://dx.doi.org/10.1090/mcom/3939

Costa E; Harvey D; Sutherland AV, 2023, 'Counting points on smooth plane quartics', Research in Number Theory, 9, http://dx.doi.org/10.1007/s40993-022-00397-8

Harvey D; Hittmeir M, 2022, 'A deterministic algorithm for finding r-power divisors', Research in Number Theory, 8, http://dx.doi.org/10.1007/s40993-022-00387-w

Harvey D; Van Der Hoeven J, 2022, 'Polynomial Multiplication over Finite Fields in Time O(n logn)', Journal of the ACM, 69, http://dx.doi.org/10.1145/3505584

Harvey D; Hittmeir M, 2022, 'A LOG-LOG SPEEDUP FOR EXPONENT ONE-FIFTH DETERMINISTIC INTEGER FACTORISATION', Mathematics of Computation, 91, pp. 1367 - 1379, http://dx.doi.org/10.1090/mcom/3708

Harvey D; van der Hoeven J, 2021, 'Integer multiplication in time O(n log n)', Annals of Mathematics, 193, pp. 563 - 617, http://dx.doi.org/10.4007/annals.2021.193.2.4

Harvey D, 2021, 'AN EXPONENT ONE-FIFTH ALGORITHM FOR DETERMINISTIC INTEGER FACTORISATION', Mathematics of Computation, 90, pp. 2937 - 2950, http://dx.doi.org/10.1090/mcom/3658

Harvey D; van der Hoeven J, 2019, 'Faster polynomial multiplication over finite fields using cyclotomic coefficient rings', Journal of Complexity, 54, http://dx.doi.org/10.1016/j.jco.2019.03.004

Harvey D; van der Hoeven J, 2019, 'Faster integer multiplication using short lattice vectors', The Open Book Series, 2, pp. 293 - 310, http://dx.doi.org/10.2140/obs.2019.2.293

Costa E; Harvey D; Kedlaya K, 2019, 'Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology', The Open Book Series, 2, pp. 221 - 238, http://dx.doi.org/10.2140/obs.2019.2.221

Harvey D; van der Hoeven J, 2018, 'On the complexity of integer matrix multiplication', Journal of Symbolic Computation, 89, pp. 1 - 8, http://dx.doi.org/10.1016/j.jsc.2017.11.001

Harvey D; Van Der Hoeven J, 2018, 'Faster integer multiplication using Plain Vanilla FFT primes', Mathematics of Computation, 88, pp. 501 - 514, http://dx.doi.org/10.1090/mcom/3328

Harvey D; Van Der Hoeven J; Lecerf G, 2017, 'Faster polynomial multiplication over finite fields', Journal of the ACM, 63, http://dx.doi.org/10.1145/3005344

Hart W; Harvey D; Ong W, 2017, 'Irregular primes to two billion', Mathematics of Computation, 86, pp. 3031 - 3049, http://dx.doi.org/10.1090/mcom/3211

Harvey D; van der Hoeven J; Lecerf G, 2016, 'Even faster integer multiplication', Journal of Complexity, 36, pp. 1 - 30, http://dx.doi.org/10.1016/j.jco.2016.03.001

Harvey D, 2015, 'Computing zeta functions of arithmetic schemes', Proceedings of the London Mathematical Society, 111, pp. 1379 - 1401, http://dx.doi.org/10.1112/plms/pdv056

Costa E; Gerbicz R; Harvey D, 2014, 'A search for Wilson primes', Mathematics of Computation, 83, pp. 3071 - 3091, http://dx.doi.org/10.1090/S0025-5718-2014-02800-7

Harvey D, 2014, 'A subquadratic algorithm for computing the n-th Bernoulli number', Mathematics of Computation, 83, pp. 2471 - 2477, http://dx.doi.org/10.1090/S0025-5718-2014-02832-9

Harvey D; Sutherland AV, 2014, 'Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time', LMS Journal of Computation and Mathematics, 17, pp. 257 - 273, http://dx.doi.org/10.1112/S1461157014000187

Harvey D, 2014, 'Counting points on hyperelliptic curves in average polynomial time', Annals of Mathematics, 179, pp. 783 - 803, http://dx.doi.org/10.4007/annals.2014.179.2.7

Harvey D, 2014, 'Faster arithmetic for number-theoretic transforms', Journal of Symbolic Computation, 60, pp. 113 - 119, http://dx.doi.org/10.1016/j.jsc.2013.09.002

Costa E; Harvey D, 2014, 'Faster deterministic integer factorization', Mathematics of Computation, 83, pp. 339 - 345, http://dx.doi.org/10.1090/S0025-5718-2013-02707-X

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

Harvey D; Hassett B; Tschinkel Y, 2012, 'Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces', Communications on Pure and Applied Mathematics, 65, pp. 264 - 286, http://dx.doi.org/10.1002/cpa.20384

Harvey D, 2012, 'The Karatsuba integer middle product', Journal of Symbolic Computation, 47, pp. 954 - 967, http://dx.doi.org/10.1016/j.jsc.2012.02.001

Harvey D, 2011, 'Faster algorithms for the square root and reciprocal of power series', Mathematics of Computation, 80, pp. 387 - 394, http://dx.doi.org/10.1090/S0025-5718-2010-02392-0

Buhler JP; Harvey D, 2011, 'Irregular primes to 163 million', Mathematics of Computation, 80, pp. 2435 - 2444, http://dx.doi.org/10.1090/S0025-5718-2011-02461-0

Harvey D, 2010, 'A multimodular algorithm for computing Bernoulli numbers', Mathematics of Computation, 79, pp. 2361 - 2370, http://dx.doi.org/10.1090/S0025-5718-2010-02367-1

Harvey D, 2009, 'A cache-friendly truncated FFT', Theoretical Computer Science, 410, pp. 2649 - 2658, http://dx.doi.org/10.1016/j.tcs.2009.03.014

Harvey D, 2009, 'Faster polynomial multiplication via multipoint Kronecker substitution', Journal of Symbolic Computation, 44, pp. 1502 - 1510, http://dx.doi.org/10.1016/j.jsc.2009.05.004

Harvey D, 2008, 'Efficient computation of p-adic heights', LMS Journal of Computation and Mathematics, 11, pp. 40 - 59, http://dx.doi.org/10.1112/S1461157000000528

Harvey D, 2007, 'Kedlaya's algorithm in larger characteristic', International Mathematics Research Notices, 2007, pp. rnm095, http://dx.doi.org/10.1093/imrn/rnm095

Harvey D, 2004, 'Selberg's Symmetry Formula', Expositiones Mathematicae, 22, pp. 185 - 195, http://dx.doi.org/10.1016/S0723-0869(04)80011-2

Harvey DM; Harvey D, 2002, 'The `Happy End` problem', Parabola, 38, pp. 5 - 9

Conference Papers

Harvey D; Massierer M; Sutherland AV, 2016, 'Computing L-series of geometrically hyperelliptic curves of genus three', in LMS Journal of Computation and Mathematics, University of Kaiserslautern, Germany, pp. 220 - 234, presented at Algorithmic Number Theory Symposium XII, University of Kaiserslautern, Germany, 29 August 2016 - 02 September 2016, http://dx.doi.org/10.1112/S1461157016000383

Harvey D; Van Der Hoeven J; Lecerf G, 2016, 'Fast polynomial multiplication over F2⁶⁰', in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 255 - 262, http://dx.doi.org/10.1145/2930889.2930920

Harvey D; Sutherland AV, 2016, 'Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II', pp. 127 - 147, http://dx.doi.org/10.1090/conm/663/13352

Harvey D; Zimmermann P, 2011, 'Short division of long integers', in 20th IEEE Symposium on Computer Arithmetic (ARITH 20), IEEE, Tuebingen, pp. 7 - 14, presented at 20th IEEE Symposium on Computer Arithmetic, Tuebingen, http://dx.doi.org/10.1109/ARITH.2011.11

Harvey DM; Roche DS, 2010, 'An in-place truncated fourier transform and applications to polynomial multiplication', in ISSAC '10 Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Munich, Germany, pp. 325 - 329, presented at ISSAC International Symposium on Symbolic and Algebraic Computation, Munich, Germany, 25 July 2010 - 28 July 2010, http://dx.doi.org/10.1145/1837934.1837996

Preprints

Harvey D; Hittmeir M, 2022, A deterministic algorithm for finding $r$-power divisors, http://dx.doi.org/10.48550/arxiv.2202.12401

Harvey D; Hittmeir M, 2021, A log-log speedup for exponent one-fifth deterministic integer factorisation, http://dx.doi.org/10.48550/arxiv.2105.11105

Harvey D; van der Hoeven J, 2018, Faster integer multiplication using short lattice vectors, http://dx.doi.org/10.48550/arxiv.1802.07932

Harvey D; Massierer M; Sutherland AV, 2016, Computing L-series of geometrically hyperelliptic curves of genus three, http://dx.doi.org/10.48550/arxiv.1605.04708

Harvey D; van der Hoeven J; Lecerf G, 2014, Even faster integer multiplication, http://dx.doi.org/10.48550/arxiv.1407.3360

Harvey D; van der Hoeven J; Lecerf G, 2014, Faster polynomial multiplication over finite fields, http://dx.doi.org/10.48550/arxiv.1407.3361

Harvey D; Sutherland AV, 2014, Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, http://dx.doi.org/10.48550/arxiv.1402.3246

Costa E; Gerbicz R; Harvey D, 2012, A search for Wilson primes, http://dx.doi.org/10.48550/arxiv.1209.3436

Harvey D, 2012, Faster arithmetic for number-theoretic transforms, http://dx.doi.org/10.48550/arxiv.1205.2926

Brent RP; Harvey D, 2011, Fast computation of Bernoulli, Tangent and Secant numbers, http://dx.doi.org/10.48550/arxiv.1108.0286

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