Lillian Pierce Publications Research Teaching Community Duke Activities Profile Lillian Pierce Publications Preprints The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter, Guth] (Bourbaki Seminar, June 2017) (abstract) (arXiv) (seminar) Endpoint Sobolev and BV Continuity for Maximal Operators with co-authors E. Carneiro and J. Madrid (submitted) Publications On $$\ell$$-torsion in class groups of number fields with co-authors J. Ellenberg and M. Matchett Wood Algebra and Number Theory, to appear. (abstract) (arXiv) A polynomial Carleson operator along the paraboloid with co-author Po-Lam Yung Revista Mat. Ibero., to appear. (abstract) (arXiv) Polynomial Carleson operators along monomial curves in the plane with co-authors Shaoming Guo, Joris Roos, Po-Lam Yung Journal of Geometric Analysis, to appear. (abstract) (arXiv) Averages and moments associated to class numbers of imaginary quadratic fields with co-author D.R. Heath-Brown Compositio. Math., to appear. (abstract) (arXiv) Representations of integers by systems of three quadratic forms with co-authors D. Schindler and M. Matchett Wood Proceedings of the London Mathematical Society (2016) doi: 10.1112/plms/pdw027 (abstract) (arXiv) (journal) Burgess bounds for multi-dimensional short mixed character sums Journal of Number Theory, 163 (2016) 172-210. (abstract) (arXiv) (journal) Lower bounds for the truncated Hilbert transform with co-authors R. Alaifari and S. Steinerberger Revista Mat. Ibero., 32, no. 1 (2016) 23 - 56. (abstract) (arXiv) (journal) Burgess bounds for short mixed character sums with co-author D.R. Heath-Brown Journal of the London Math. Soc., 91, no. 3 (2015) 693-708. (abstract) (arXiv) (journal) Simultaneous integer values of pairs of quadratic forms with co-author D.R. Heath-Brown J. Reine Angew. Math., in press (abstract) (arXiv) (journal) Counting rational points on smooth cyclic covers with co-author D.R. Heath-Brown Journal of Number Theory, 132 (2012), pp. 1741-1757. (abstract) (pdf) (arXiv) (journal) On a discrete version of Tanaka's theorem for maximal functions with co-authors Jonathan Bober, Emanuel Carneiro, and Kevin Hughes Proceedings of the Amer. Math. Soc. 140 (2012) 1669-1680. (abstract) (journal) revised version on (arXiv) A note on discrete fractional integral operators on the Heisenberg group Internat. Math. Res. Not. Vol. 2012, No. 1, (2012) 17-33. (abstract) (pdf) (journal link) Discrete fractional Radon transforms and quadratic forms Duke Math. Journal 161, No. 1 (2012) 69-106. Correction 162 (2013) 1203-1204. (abstract) (pdf) On discrete fractional integral operators and mean values of Weyl sums Bull. London Math. Soc., 43 (2011) 597-612. (abstract) (pdf) (journal) A note on discrete twisted singular Radon transforms Mathematical Research Letters 17, no. 4 (2010) 701-720. (abstract) (pdf) (journal) A bound for the 3-part of class numbers of quadratic fields by means of the square sieve Forum Math. 18 (2006) no. 4, 677-698. (abstract) (pdf) (journal) Companion paper by N. M. Katz On a question of Lillian Pierce by Nicholas M. Katz Forum Math. 18 (2006) no. 4, 699-710. (pdf) The 3-part of class numbers of quadratic fields J. London Math. Soc. (2) 71 (2005) 579-598. (abstract) (pdf) (journal) Note: preprints may differ slightly from final published versions. Other writings Princeton Lectures in Analysis, by Elias M. Stein and Rami Shakarchi — A Book Review Book Review in the Notices of the AMS, May 2012 issue Reviewed by Charles Fefferman and Robert Fefferman, with contributions from Paul Hagelstein, Nataśa Pavlović, and Lillian Pierce Theses Discrete Analogues in Harmonic Analysis PhD Thesis, Princeton University, 2009 Advisor: E. M. Stein The 3-Part of Class Numbers of Quadratic Fields MSc Thesis, Oxford University, 2004 Advisor: D. R. Heath-Brown The Pair Correlation of the Zeroes of the Riemann Zeta Function Undergraduate Senior Thesis, Princeton University, 2002 Advisor: E. M. Stein