Prof. Dr. Harald Andrés Helfgott

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  • 2022 | Journal Article
    ​ ​Optimality for the two-parameter quadratic sieve​
    Carneiro, E.; Chirre, A.; Helfgott, H. A.   & Mejía-Cordero, J.​ (2022) 
    Acta Arithmetica,.​ DOI: https://doi.org/10.4064/aa201018-5-1 
    ​Details  DOI 
  • 2022 | Journal Article | 
    ​ ​Summing μ(n) : a faster elementary algorithm​
    Helfgott, H. A.   & Thompson, L.​ (2022) 
    Research in Number Theory, 9(1).​ DOI: https://doi.org/10.1007/s40993-022-00408-8 
    ​Details  DOI 
  • 2020 | Journal Article
    ​ ​An improved sieve of Eratosthenes​
    Helfgott, H. A. ​ (2020) 
    Mathematics of Computation, 89(321) pp. 333​-350​.​ DOI: https://doi.org/10.1090/mcom/3438 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Isomorphismes de graphes en temps quasi-polynomial (d’après Babai et Luks, Weisfeiler-Leman, ...)​
    Helfgott, H. A. ​ (2019) 
    Astérisque, 407 pp. 135​-182​.​ DOI: https://doi.org/10.24033/ast.1063 
    ​Details  DOI  arXiv 
  • 2019 | Book Chapter
    ​ ​Growth in Linear Algebraic Groups and Permutation Groups: Towards a Unified Perspective​
    Helfgott, H. A. ​ (2019)
    In:​Campbell, C. M.; Parker, C. W.; Quick, M. R.; Robertson, E. F.; Roney-Dougal, C. M.​ (Eds.), Groups St Andrews 2017 in Birmingham pp. 300​-345. ​Cambridge: ​Cambridge University Press. DOI: https://doi.org/10.1017/9781108692397.014 
    ​Details  DOI 
  • 2019 | Journal Article
    ​ ​Soficity, short cycles, and the Higman group​
    Helfgott, H. A.   & Juschenko, K.​ (2019) 
    Transactions of the American Mathematical Society, 371(4) pp. 2771​-2795​.​ DOI: https://doi.org/10.1090/tran/2019-371-04 
    ​Details  DOI  arXiv 
  • 2015 | Journal Article
    ​ ​Random generators of the symmetric group: diameter, mixing time and spectral gap​
    Helfgott, H. A. ; Seress, Á. & Zuk, A.​ (2015) 
    Journal of Algebra, 421 pp. 349​-368​.​
    ​Details  arXiv 
  • 2015 | Journal Article
    ​ ​On the dimension of additive sets​
    Candela, P. & Helfgott, H. A. ​ (2015) 
    Acta Arithmetica, 167(1) pp. 91​-100​.​ DOI: https://doi.org/10.4064/aa167-1-5 
    ​Details  DOI 
  • 2015 | Preprint
    ​ ​The ternary Goldbach problem​
    Helfgott, H. A. ​ (2015)
    ​Details  arXiv 
  • 2015 | Journal Article
    ​ ​Growth in groups: ideas and perspectives​
    Helfgott, H. A. ​ (2015) 
    Bulletin of the American Mathematical Society, 52(3) pp. 357​-413​.​ DOI: https://doi.org/10.1090/s0273-0979-2015-01475-8 
    ​Details  DOI 
  • 2015 | Journal Article | 
    ​ ​On growth in an abstract plane​
    Gill, N.; Helfgott, H. A.   & Rudnev, M.​ (2015) 
    Proceedings of the American Mathematical Society, 143(8) pp. 3593​-3602​.​ DOI: https://doi.org/10.1090/proc/12309 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​Square-free values of f(p), f cubic​
    Helfgott, H. A. ​ (2014) 
    Acta Mathematica, 213(1) pp. 107​-135​.​ DOI: https://doi.org/10.1007/s11511-014-0117-2 
    ​Details  DOI 
  • 2014 | Journal Article
    ​ ​On the diameter of permutation groups​
    Helfgott, H. A.   & Seress, Á.​ (2014) 
    Annals of Mathematics, 179(2) pp. 611​-658​.​ DOI: https://doi.org/10.4007/annals.2014.179.2.4 
    ​Details  DOI 
  • 2013 | Preprint
    ​ ​The ternary Goldbach conjecture is true​
    Helfgott, H. A. ​ (2013)
    ​Details  arXiv 
  • 2013 | Preprint
    ​ ​Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30​
    Helfgott, H. A.  & Platt, D. J.​ (2013)
    ​Details  arXiv 
  • 2013 | Preprint
    ​ ​Major arcs for Goldbach's problem​
    Helfgott, H. A. ​ (2013)
    ​Details  arXiv 
  • 2013 | Journal Article | 
    ​ ​Bounds on the diameter of Cayley graphs of the symmetric group​
    Bamberg, J.; Gill, N.; Hayes, T. P.; Helfgott, H. A. ; Seress, Á. & Spiga, P.​ (2013) 
    Journal of Algebraic Combinatorics, 40(1) pp. 1​-22​.​ DOI: https://doi.org/10.1007/s10801-013-0476-3 
    ​Details  DOI  arXiv 
  • 2012 | Preprint
    ​ ​Minor arcs for Goldbach's problem​
    Helfgott, H. A. ​ (2012)
    ​Details  arXiv 
  • 2011 | Journal Article
    ​ ​Growth in SL3(ℤ/pℤ)​
    Helfgott, H. A. ​ (2011) 
    Journal of the European Mathematical Society, 13(3) pp. 761​-851​.​ DOI: https://doi.org/10.4171/jems/267 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​An Explicit Incidence Theorem In 𝔽p​
    Helfgott, H. A.   & Rudnev, M.​ (2011) 
    Mathematika, 57(01) pp. 135​-145​.​ DOI: https://doi.org/10.1112/s0025579310001208 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​Improving Roth's Theorem in the Primes​
    Helfgott, H. A.   & Roton, A. de​ (2011) 
    International Mathematics Research Notices, 4 pp. 767​-783​.​ DOI: https://doi.org/10.1093/imrn/rnq108 
    ​Details  DOI 
  • 2011 | Journal Article
    ​ ​Deterministic methods to find primes​
    Tao, T.; Croot, E. & Helfgott, H. A. ​ (2011) 
    Mathematics of Computation, 81(278) pp. 1233​-1246​.​ DOI: https://doi.org/10.1090/s0025-5718-2011-02542-1 
    ​Details  DOI  arXiv 
  • 2011 | Preprint
    ​ ​Groupes, courbes et croissance​
    Helfgott, H. A. ​ (2011)
    ​Details  arXiv 
  • 2010 | Preprint
    ​ ​Growth in solvable subgroups of GL_r(Z/pZ)​
    Gill, N.& Helfgott, H. A. ​ (2010)
    ​Details  arXiv 
  • 2010 | Journal Article
    ​ ​Growth of Small Generating Sets in SLn(Z/pZ)​
    Gill, N. & Helfgott, H. A. ​ (2010) 
    International Mathematics Research Notices,.​ DOI: https://doi.org/10.1093/imrn/rnq244 
    ​Details  DOI  arXiv 
  • 2009 | Preprint
    ​ ​Azar y Aritmetica​
    Helfgott, H. A. ​ (2009)
    ​Details  arXiv 
  • 2009 | Book Chapter
    ​ ​How small must ill-distributed sets be?​
    Helfgott, H. A.  & Venkatesh, A.​ (2009)
    In:​Chen, W. W. L.​ (Ed.), Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday pp. 224​-234. ​Cambridge University Press.
    ​Details 
  • 2008 | Journal Article
    ​ ​Growth and Generation in SL_2(Z/pZ)​
    Helfgott, H. A. ​ (2008) 
    Annals of Mathematics, 167(2) pp. 601​-623​.​ DOI: https://doi.org/10.4007/annals.2008.167.601 
    ​Details  DOI 
  • 2007 | Journal Article
    ​ ​Power-free values, large deviations, and integer points on irrational curves​
    Helfgott, H. A. ​ (2007) 
    Journal de Théorie des Nombres de Bordeaux, 19(2) pp. 433​-472​.​ DOI: https://doi.org/10.5802/jtnb.596 
    ​Details  DOI 
  • 2007 | Preprint
    ​ ​Power-free values, repulsion between points, differing beliefs and the existence of error​
    Helfgott, H. A. ​ (2007)
    ​Details  arXiv 
  • 2006 | Journal Article
    ​ ​Integral points on elliptic curves and 3-torsion in class groups​
    Helfgott, H. A.   & Venkatesh, A.​ (2006) 
    Journal of the American Mathematical Society, 19(3) pp. 527​-550​.​ DOI: https://doi.org/10.1090/s0894-0347-06-00515-7 
    ​Details  DOI 
  • 2006 | Journal Article
    ​ ​THE PARITY PROBLEM FOR REDUCIBLE CUBIC FORMS​
    Helfgott, H. A. ​ (2006) 
    Journal of the London Mathematical Society, 73(02) pp. 415​-435​.​ DOI: https://doi.org/10.1112/s0024610706022629 
    ​Details  DOI  arXiv 
  • 2005 | Journal Article
    ​ ​Root numbers and ranks in positive characteristic​
    Conrad, B.; Conrad, K. & Helfgott, H. ​ (2005) 
    Advances in Mathematics, 198(2) pp. 684​-731​.​ DOI: https://doi.org/10.1016/j.aim.2005.06.013 
    ​Details  DOI 
  • 2004 | Preprint
    ​ ​On the behaviour of root numbers in families of elliptic curves​
    Helfgott, H. A. ​ (2004)
    ​Details  arXiv 
  • 2004 | Journal Article
    ​ ​On the square-free sieve​
    Helfgott, H. A. ​ (2004) 
    Acta Arithmetica, 115(4) pp. 349​-402​.​
    ​Details 
  • 1999 | Journal Article
    ​ ​Enumeration of Tilings of Diamonds and Hexagons with Defects​
    Helfgott, H. A.   & Gessel, I. M.​ (1999) 
    The Electronic Journal of Combinatoric, 6.​
    ​Details 

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