Lillian Pierce
Publications


Preprints

On Superorthogonality
(submitted)
with an appendix by Emmanuel Kowalski

(abstract) (arXiv)

Burgess bounds for short character sums evaluated at forms II: the mixed case
(submitted)

(abstract) (arXiv)

Reversing a philosophy: from counting to square functions and decoupling
with P. Gressman, S. Guo, J. Roos, and P-Y Yung
(submitted)

(abstract) (arXiv)

On a conjecture for \(\ell\)-torsion in class groups of number fields: from the perspective of moments
with C. Turnage-Butterbaugh and M. M. Wood
(submitted)

(abstract) (arXiv)

Elias M. Stein (1931-2018)
Memorial for the Notices of the AMS


Publications

Analysis and Applications: The Mathematical Work of Elias Stein
Bulletin of the AMS (published online March 2020).
by C. Fefferman, A. Ionescu, T. Tao and S. Wainger; with contributions from L. Lanzani, A. Magyar, M. Mirek, A. Nagel, D. H. Phong, L. Pierce, F. Ricci, C. Sogge, B. Street.

(journal)

On Bourgain's counterexample for the Schrödinger maximal function
Quarterly Journal of Mathematics (accepted)

(abstract) (arXiv)

Burgess bounds for short character sums evaluated at forms
with J. Xu
Algebra and Number Theory (accepted)

(abstract) (arXiv)

On matrix rearrangement inequalities
with R. Alaifari, X. Cheng, and S. Steinerberger
Proceedings of the AMS 148 (5) (2020) 1835-1848.

(abstract) (arXiv)

An effective Chebotarev density theorem for families of number fields, with an application to \(\ell\)-torsion in class groups
with C. Turnage-Butterbaugh and M. M. Wood
Inventiones 219 (2) (2020) 701-778.

(abstract) (arXiv)

On torsion subgroups in class groups of number fields,
JMM 2019 Sampler, Notices of the AMS, vol. 66 no. 1, January (2019) 97-98

A polynomial Carleson operator along the paraboloid
with co-author Po-Lam Yung
Revista Mat. Ibero. 35 (2) (2019) 339-422.

(abstract) (arXiv)

The Vinogradov Mean Value Theorem
[after Wooley, and Bourgain, Demeter, Guth]

(Bourbaki Seminar, volume 69, 2016/2017, expose 1134)
Asterisque (2019) volume 407.

(abstract) (arXiv) (seminar)

Endpoint Sobolev and BV Continuity for Maximal Operators
with co-authors E. Carneiro and J. Madrid
J. Functional Analysis, 273 (2017) 3262-3294.
(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 (2017) 1-36.

(abstract) (arXiv)

On \(\ell\)-torsion in class groups of number fields
with co-authors J. Ellenberg and M. Matchett Wood
Algebra and Number Theory 11 (8) Jan (2017) 1739-1778.

(abstract) (arXiv)

Averages and moments associated to class numbers of imaginary quadratic fields
with co-author D.R. Heath-Brown
Compositio. Math. 153 (2017) 2287-2309.

(abstract) (arXiv)

Simultaneous integer values of pairs of quadratic forms
with co-author D.R. Heath-Brown
J. Reine Angew. Math. (Crelle) 727 (2017) 2287-2309.

(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)

Representations of integers by systems of three quadratic forms
with co-authors D. Schindler and M. Matchett Wood
Proceedings of the London Mathematical Society (3) 113 (2016) 289-344.

(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)

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)

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

Oberwolfach report 2016 (link)

Oberwolfach report 2014 (link)

Oberwolfach report 2013 (link)

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