
 89.
Uniform bounds for rational points on hyperelliptic fibrations
(with Dante Bonolis)
(arXiv:2007.14182)
 88.
The Hasse principle for random Fano hypersurfaces
(with P. Le Boudec and W. Sawin)
(arXiv:2006.02356)
 87.
The geometric sieve for quadrics
(with D.R. HeathBrown)
Forum Math., to appear.
(arXiv:2003.09593)
 86.
Free rational points on smooth hypersurfaces
(with W. Sawin)
Comment. Math. Helv.
95 (2020), 635659.
(arXiv:1906.08463)
 85.
Arithmetic of higherdimensional orbifolds and a mixed Waring problem (with S. Yamagishi)
Math. Zeit., to appear.
(arXiv:1902.07782)
 84.
Free rational curves on low degree hypersurfaces and the circle method
(with W. Sawin)
(arXiv:1810.06882)
 83.
Counting rational points on biquadratic hypersurfaces
(with L.Q. Hu)
Advances Math. 349 (2019), 920940.
(arXiv:1810.08426)
 82.
Density of rational points on a quadric bundle in
P^{3}x P^{3} (with D.R. HeathBrown)
Duke Math. J.
169 (2020), 30993165
(arXiv:1805.10715)
 81.
Counting rational points on quadric surfaces (with D.R. HeathBrown)
Discrete Analysis 2018:15, 29 pp.
 80.
A geometric version of the circle method
(with W. Sawin)
Annals of Math. 191 (2020), 893948.
(arXiv:1711.10451)
 79.
Averages of arithmetic functions over principal ideals (with E. Sofos)
Int. J. Number Theory 15 (2019), 547567.
(arXiv:1706.04331)
 78.
Sieving rational points on varieties (with D. Loughran)
Trans. Amer. Math. Soc. 371 (2019), 57575785.
(arXiv:1705.01999)
 77.
Many cubic surfaces have rational points
Mathematika
63 (2017), 818839.
(arXiv:1701.00525)
 76.
Rational curves on smooth hypersurfaces of low degree (with
P. Vishe)
Algebra & Number Theory
11 (2017), 16571675.
(arXiv:1611.00553)
 75.
Counting rational points on quartic del Pezzo surfaces with a rational
conic
(with E. Sofos).
Math. Annalen 373
(2019),
9771016.
(arXiv:1609.09057)
 74.
Twisted Linnik implies optimal covering exponent for
S^{3} (with V. Kumaraswamy and
R. Steiner)
IMRN
2019, no. 1, 140164.
(arXiv:1609.06097)
 73.
Powerfree values of polynomials on symmetric varieties (with
A. Gorodnik)
Proc. London Math. Soc. 114 (2017), 10441080.
(arXiv:1606.06342)
 72.
How often does the Hasse principle hold?
Algebraic Geometry: Salt Lake City 2015,
Proc. Symposia Pure Math.
97.2 (2018), AMS, 89102.
 71.
Squarefree values of reducible polynomials
(with A. Booker); (see extended
data)
Discrete Analysis 2016:8, 16pp.
 70.
A transference approach to a Rothtype theorem in the squares
(with S. Prendiville)
IMRN 2017, no. 7, 22192248.
(arXiv:1510.00136)
 69.
Strong approximation and a conjecture of Harpaz and Wittenberg
(with D. Schindler)
IMRN
2019, no. 14, 43404369.
(arXiv:1509.07744)
 68.
Failures of weak approximation in families
(with M. Bright and D. Loughran)
Compositio Math. 152 (2016), 14351475.
(arXiv:1506.01817)
 67.
Rational points on cubic hypersurfaces over
F_{q}(t)
(with P. Vishe)
GAFA 25 (2015), 671732.
(arXiv:1502.00772)
 66.
The proportion of failures of the Hasse norm principle
(with R. Newton)
Mathematika 62 (2016), 337347.
(arXiv:1411.7775)
 65.
Counting rational points on the Cayley ruled cubic
(with R. de la Bretèche and P. Salberger)
Eur. J. Math. 2 (2016), 5572.
(arXiv:1410.3855)
 64.
Forms in many variables and differing degrees
(with D.R. HeathBrown)
J. Eur. Math. Soc. 9 (2017), 357394.
(arXiv:1403.5937)
 63.
Improvements in Birch's theorem on forms in many variables (with
S. Prendiville)
Journal reine angew. Math. 731
(2017), 203234.
(arXiv:1402.4489)
 62.
A survey of applications of the circle method to rational points
Arithmetic and geometry,
London Math. Soc. Lecture Note Ser. 420 (2015), CUP, 89113.
 61.
Effective Ratner theorem for ASL(2,R) and gaps in √n modulo
1 (with I. Vinogradov)
J. London Math. Soc. 94 (2016), 6184.
(arXiv:1311.6387)
 60.
Varieties with too many rational points
(with D. Loughran)
Math. Zeit. 285 (2017), 12491267.
(arXiv:1311.5755)
 59.
Counting rational points on del Pezzo surfaces with a conic bundle structure
(with M. Swarbrick Jones)
Acta Arithmetica 163 (2014), 271298.
(arXiv:1311.1665)
 58.
Rational points on intersections of cubic and quadric hypersurfaces
(with R. Dietmann and D.R. HeathBrown)
J. Inst. Math. Jussieu 14 (2015), 703749.
(arXiv:1309.0147)
 58a.
Corrigendum for "Rational points on intersections of cubic and quadric hypersurfaces"
J. Inst. Math. Jussieu 14 (2015), 751.
 57.
Norm forms for arbitrary number fields as products of linear
polynomials (with L. Matthiesen)
Ann. Sci. Ecole Norm. Sup. 50 (2017), 13751438.
(arXiv:1307.7641)
 56.
The polynomial sieve and equal sums of like
polynomials
IMRN 2015 (2015), 19872019.
(arXiv:1306.6767)
 55.
Pairs of diagonal quadratic forms and linear correlations
among sums of two squares (with R. Munshi)
Forum Math. 27 (2015), 20252050.
(arXiv:1302.2434)
 54.
Contreexemples au principe de Hasse pour certains tores coflasques (with R. de la Bretèche)
J. Théorie Nombres Bordeaux 26
(2014), 2544.
(arXiv:1210.4236)
 53.
Rational points on pencils of conics and quadrics with many degenerate fibres
(with L. Matthiesen and A. Skorobogatov)
Annals of Math. 180 (2014), 381402.
(arXiv:1209.0207)
 52.
Cubic hypersurfaces and a version of the circle method for number fields
(with P. Vishe)
Duke Math. J. 163 (2014), 18251883.
(arXiv:1207.2385)
 51.
Density of Châtelet surfaces failing the Hasse principle
(with R. de la Bretèche)
Proc. London Math. Soc.
108 (2014), 10301078.
(arXiv:1210.4010)
 50.
Incomplete Kloosterman sums and multiplicative inverses in short
intervals
(with A. Haynes)
Int. J. Number Theory 9 (2013), 481486.
(arXiv:1204.6374)
 49.
Quadratic polynomials represented by norm forms
(with D.R. HeathBrown)
GAFA 22 (2012), 11241190.
(arXiv:1109.0232)
 48.
Rational points on singular intersections of quadrics
(with R. Munshi)
Compositio Math. 149 (2013), 14571494.
(arXiv:1108.1902)
 47.
Sums of three squareful numbers
(with K. Van Valckenborgh)
Experimental Mathematics 21 (2012), 204211.
(arXiv:1106.4472)
 46.
Inhomogeneous quadratic congruences
(with S. Baier)
Functiones et Approximatio 47 (2012), 267286.
(arXiv:1105.1915)
 45.
Averages of shifted convolutions of d3(n)
(with S. Baier, G. Marasingha and L. Zhao)
Proc. Edinburgh Math. Soc. 55 (2012), 551576.
(arXiv:1101.5464)
 44.
Inhomogeneous cubic congruences and
rational points on del Pezzo surfaces
(with S. Baier)
Journal reine angew. Math. 680 (2013), 69151.
(arXiv:1011.3434)
 43.
Powerfree values of polynomials
Arch. Math. 96 (2011), 139150.
 42.
Binary forms as sums of two squares and Châtelet
surfaces (with R. de la Bretèche)
Israel J. Math. 191 (2012), 9731012.
(arXiv:1006.5859)
 41.
The divisor problem for binary cubic forms
J. Théorie Nombres Bordeaux 23 (2011), 579602.
(arXiv:1006.3476)
 40.
The LangWeil estimate for cubic hypersurfaces
Canad. Math. Bull. 56 (2013), 500502.
 39.
On Manin's conjecture for a family of Châtelet
surfaces (with R. de la Bretèche and
E. Peyre)
Annals of Math. 175 (2012), 297343.
(arXiv:1002.0255)
 38.
The number of representations of rationals as a sum of unit fractions (with C. Elsholtz)
Illinois J. Math. 55 (2011), 685696.
 37.
Least zero of a cubic form
(with R. Dietmann and P.D.T.A. Elliott)
Math. Annalen 352 (2011), 745778.
(arXiv:0907.5261)
 36.
Quantitative
arithmetic of projective varieties
Progress in Math. 277, Birkhäuser, 2009.
 35.
Linear growth for Châtelet surfaces
Math. Annalen 346 (2010), 4150.
(arXiv:0901.1963)
 34.
Manin's conjecture for quartic del Pezzo surfaces with a
conic fibration (with R. de la Bretèche)
Duke Math. J. 160 (2011), 169.
 33.
Le problème des diviseurs pour des formes binaires de
degré 4 (with R. de la Bretèche)
Journal reine angew. Math.
646 (2010), 144.
 32.
Rational points on cubic hypersurfaces that
split off a form
Compositio Math. 146 (2010),
853885.
 31.
Manin's conjecture for a cubic surface with D_5 singularity
(with U. Derenthal)
IMRN 14 (2009),
26202647.
 30.
Manin's conjecture for a quartic del Pezzo surface with
A_4 singularity (with U. Derenthal)
Ann. Inst. Fourier 59 (2009),
12311265.
 29.
Recent progress on the quantitative arithmetic of del
Pezzo surfaces
Proceedings of the 5th ChinaJapan Number Theory Conference
(Osaka, 2731 August 2008), World
Scientific (2010), 119.
 28.
Solubility of Fermat equations (with R. Dietmann)
Quadratic forms  algebra, arithmetic and geometry,
Contemporary Math. 493 (2009), 99106.
 27.
Binary linear forms as sums of two squares (with
R. de la
Bretèche)
Compositio Math. 144 (2008),
13751402.
 26.
Rational points on quartic hypersurfaces (with
D.R. HeathBrown)
Journal reine angew. Math.
629 (2009), 3788.
 25.
Integral points on cubic hypersurfaces (with
D.R. HeathBrown)
Analytic Number Theory: Essays in honour of Klaus
Roth, CUP (2009), 7590.
 24.
On the representation of integers by quadratic forms
(with R. Dietmann)
Proc. London Math. Soc. 96
(2008), 389416.
 23a.
Corrigendum for "Counting rational points on cubic hypersurfaces"
Mathematika 60 (2014), 101107.
 23.
Counting rational points on cubic hypersurfaces
Mathematika 54 (2007), 93112.
 22.
On Manin's conjecture for singular del Pezzo surfaces of
degree four, II (with R. de la Bretèche)
Math. Proc. Camb. Phil. Soc.
143 (2007), 579605.
 21.
An overview of Manin's conjecture for del Pezzo surfaces
Analytic number theory  A tribute to Gauss and
Dirichlet
(Goettingen, 20th June  24th June, 2005), Clay
Mathematics Proceedings 7 (2007), 3956.
 20.
Density of integer solutions to diagonal quadratic
forms.
Monatsh. Math. 152 (2007), 1338.
 19.
On Manin's conjecture for a certain singular cubic
surface (with R. de la Bretèche and U. Derenthal)
Ann. Sci. Ecole Norm. Sup. 40 (2007), 150.
 18.
Simultaneous equal sums of three powers (with D.R. HeathBrown)
Proc. of the session on Diophantine geometry
(Pisa, 1st April  30th July, 2005), CRM series
4 (2007), 93100.
 17.
On Manin's conjecture for singular del Pezzo surfaces of degree four,
I (with R. de la Bretèche)
Michigan Math. J.
55 (2007), 5180.
 16.
Sums of arithmetic functions over values of binary
forms (with R. de la Bretèche)
Acta Arith.
125 (2006), 291304.
 15.
The density of rational points on nonsingular
hypersurfaces, II (with D.R. HeathBrown)
Proc. London Math. Soc.
93 (2006), 273303.
 14.
The density of rational points on a certain singular cubic surface
J. Number Theory 119 (2006), 242283.
 13.
The density of rational points on
nonsingular hypersurfaces, I (with D.R. HeathBrown)
Bull. London Math. Soc. 38 (2006), 401410.
 12.
Counting rational points on algebraic
varieties (with D.R. HeathBrown and P. Salberger)
Duke Math. J. 132 (2006), 545578.
 11.
Equal sums of like polynomials
Bull. London Math. Soc. 37 (2005), 801808.
 10.
Counting rational points on
hypersurfaces (with D.R. HeathBrown)
Journal reine angew. Math. 584
(2005), 83115.
 9. H. Davenport,
Analytic methods for Diophantine equations and
Diophantine inequalities
2nd ed., edited and
prepared for publication by T.D. Browning. CUP, 2005.
 8.
Plane curves in boxes and equal sums
of two powers (with D.R. HeathBrown)
Math. Zeit. 251 (2005), 233247.
 7.
Equal sums of three powers (with D.R. HeathBrown)
Invent. Math. 157 (2004), 553573.
 6.
Counting rational points on del Pezzo surfaces of degree
five.
Session on analytic
number theory and Diophantine equations, Bonn. Math. Schrift. 360 (2003).
 5.
Sums of four biquadrates
Math. Proc. Camb. Phil. Soc. 134 (2003),
385395.
 4.
Counting rational points on cubic and quartic
surfaces
Acta Arith. 108 (2003), 275295.
 3.
A note on the distribution of rational points on
threefolds
Quart. J. Math. 54 (2003), 3339.
 2.
Counting rational points on
diagonal quadratic surfaces
Quart. J. Math. 54 (2003), 1131.
 1. Equal sums of two kth
powers
J. Number Theory 96 (2002), 293318.


