Tim Browning - research

109. Solubility of a resultant equation and applications (with S. Chan)
(arXiv:2411.09264)
108. Bounds on the exceptional set in the abc conjecture (with J.D. Lichtman and J. Teräväinen)
(arXiv:2410.12234)
107. Pairs of commuting integer matrices (with W. Sawin and V.Y. Wang)
(arXiv:2409.01920)
106. Counting integer points on affine surfaces with a side condition (with M. Verzobio)
(arXiv:2408.11453)
105. Optimal sums of cubes in F_q[t] (with J. Glas and V.Y. Wang)
(arXiv:2408.03668)
104. Integral points on cubic surfaces: heuristics and numerics (with F. Wilsch)
(arXiv:2407.16315)
103. Rational curves on complete intersections and the circle method (With P. Vishe and S. Yamagishi)
(arXiv:2404.11123)
102. Strong divisibility sequences and sieve methods (with M. Verzobio)
Mathematika 70 (2024), Paper No. e12269, 26 pp. (arXiv:2402.19301)
101. Sums of three cubes over a function field (with J. Glas and V.Y. Wang)
(arXiv:2402.07146)
100. Almost all quadratic twists of an elliptic curve have no integral points (with S. Chan)
(arXiv:2401.04375)
99. Paucity of rational points on fibrations with multiple fibres (with J. Lyczak and A. Smeets)
Algebra & Number Theory, to appear. (arXiv:2310.01135)
98. Square-free values of random polynomials (with I. Shparlinski)
J. Number Theory 261 (2024), 220-240. (arXiv:2305.15493)
97. A motivic circle method (with M. Bilu)
(arXiv:2304.09645)
96. Generalised quadratic forms over totally real number fields (with L.B. Pierce and D. Schindler)
J. Inst. Math. Jussieu 23 (2024), 2859-2912. (arXiv:2212.11038)
95. Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1 (with E. Sofos and J. Teräväinen)
(arXiv:2212.11038)
94. Density of rational points on some quadric bundle threefolds (with D. Bonolis and Z. Huang)
Math. Annalen 390 (2024), 4123-4207. (arXiv:2204.09322)
93. Revisiting the Manin-Peyre conjecture for the split del Pezzo surface of degree 5
New York J. Math. 28 (2022), 1193-1229.
92. Local solubility for a family of quadrics over a split quadric surface (with J. Lyczak and R. Sarapin)
Involve 16 (2023), 331-342. (arXiv:2203.06881)
91. Cubic forms and the circle method
Progress in Math. 343, Birkhäuser, 2021
90. Equidistribution and freeness on Grassmannians (with T. Horesh and F. Wilsch)
Algebra & Number Theory 16 (2022), 2385-2407. (arXiv:2102.11552)
89. Uniform bounds for rational points on hyperelliptic fibrations (with D. Bonolis)
Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023), 173-204. (arXiv:2007.14182)
89a. Corrigendum for "Uniform bounds for rational points on hyperelliptic fibrations"
Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023), 2501-2504.
88. The Hasse principle for random Fano hypersurfaces (with P. Le Boudec and W. Sawin)
Annals of Math. 197 (2023), 1115-1203. (arXiv:2006.02356)
87. The geometric sieve for quadrics (with D.R. Heath-Brown)
Forum Math. 33 (2021), 147-165. (arXiv:2003.09593)
86. Free rational points on smooth hypersurfaces (with W. Sawin)
Comment. Math. Helv. 95 (2020), 635-659. (arXiv:1906.08463)
85. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem (with S. Yamagishi)
Math. Zeit. 299 (2021), 1071-1101. (arXiv:1902.07782)
84. Free rational curves on low degree hypersurfaces and the circle method (with W. Sawin)
Algebra & Number Theory 17 (2023), 719-748. (arXiv:1810.06882)
83. Counting rational points on biquadratic hypersurfaces (with L.Q. Hu)
Advances Math. 349 (2019), 920-940. (arXiv:1810.08426)
82. Density of rational points on a quadric bundle in P³x P³ (with D.R. Heath-Brown)
Duke Math. J. 169 (2020), 3099-3165 (arXiv:1805.10715)
81. Counting rational points on quadric surfaces (with D.R. Heath-Brown)
Discrete Analysis 2018:15, 29 pp.
80. A geometric version of the circle method (with W. Sawin)
Annals of Math. 191 (2020), 893-948. (arXiv:1711.10451)
79. Averages of arithmetic functions over principal ideals (with E. Sofos)
Int. J. Number Theory 15 (2019), 547-567. (arXiv:1706.04331)
78. Sieving rational points on varieties (with D. Loughran)
Trans. Amer. Math. Soc. 371 (2019), 5757-5785. (arXiv:1705.01999)
77. Many cubic surfaces have rational points
Mathematika 63 (2017), 818-839. (arXiv:1701.00525)
76. Rational curves on smooth hypersurfaces of low degree (with P. Vishe)
Algebra & Number Theory 11 (2017), 1657-1675. (arXiv:1611.00553)
75. Counting rational points on quartic del Pezzo surfaces with a rational conic (with E. Sofos).
Math. Annalen 373 (2019), 977-1016. (arXiv:1609.09057)
74. Twisted Linnik implies optimal covering exponent for S³ (with V. Kumaraswamy and R. Steiner)
IMRN 2019, no. 1, 140-164. (arXiv:1609.06097)
73. Power-free values of polynomials on symmetric varieties (with A. Gorodnik)
Proc. London Math. Soc. 114 (2017), 1044-1080. (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, 89-102.
71. Square-free values of reducible polynomials (with A. Booker); (see extended data)
Discrete Analysis 2016:8, 16pp.
70. A transference approach to a Roth-type theorem in the squares (with S. Prendiville)
IMRN 2017, no. 7, 2219-2248. (arXiv:1510.00136)
69. Strong approximation and a conjecture of Harpaz and Wittenberg (with D. Schindler)
IMRN 2019, no. 14, 4340-4369. (arXiv:1509.07744)
68. Failures of weak approximation in families (with M. Bright and D. Loughran)
Compositio Math. 152 (2016), 1435-1475. (arXiv:1506.01817)
67. Rational points on cubic hypersurfaces over F_q(t) (with P. Vishe)
GAFA 25 (2015), 671-732. (arXiv:1502.00772)
66. The proportion of failures of the Hasse norm principle (with R. Newton)
Mathematika 62 (2016), 337-347. (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), 55-72. (arXiv:1410.3855)
64. Forms in many variables and differing degrees (with D.R. Heath-Brown)
J. Eur. Math. Soc. 9 (2017), 357-394. (arXiv:1403.5937)
63. Improvements in Birch's theorem on forms in many variables (with S. Prendiville)
Journal reine angew. Math. 731 (2017), 203-234. (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, 89-113.
61. Effective Ratner theorem for ASL(2,R) and gaps in √n modulo 1 (with I. Vinogradov)
J. London Math. Soc. 94 (2016), 61-84. (arXiv:1311.6387)
60. Varieties with too many rational points (with D. Loughran)
Math. Zeit. 285 (2017), 1249-1267. (arXiv:1311.5755)
59. Counting rational points on del Pezzo surfaces with a conic bundle structure (with M. Swarbrick Jones)
Acta Arithmetica 163 (2014), 271-298. (arXiv:1311.1665)
58. Rational points on intersections of cubic and quadric hypersurfaces (with R. Dietmann and D.R. Heath-Brown)
J. Inst. Math. Jussieu 14 (2015), 703-749. (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), 1375-1438. (arXiv:1307.7641)
56. The polynomial sieve and equal sums of like polynomials
IMRN 2015 (2015), 1987-2019. (arXiv:1306.6767)
56a. Corrigendum for "The polynomial sieve and equal sums of like polynomials"
IMRN 2024 (2024), 10165-10168.
55. Pairs of diagonal quadratic forms and linear correlations among sums of two squares (with R. Munshi)
Forum Math. 27 (2015), 2025-2050. (arXiv:1302.2434)
54. Contre-exemples au principe de Hasse pour certains tores coflasques (with R. de la Bretèche)
J. Théorie Nombres Bordeaux 26 (2014), 25-44. (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), 381-402. (arXiv:1209.0207)
52. Cubic hypersurfaces and a version of the circle method for number fields (with P. Vishe)
Duke Math. J. 163 (2014), 1825-1883. (arXiv:1207.2385)
51. Density of Châtelet surfaces failing the Hasse principle (with R. de la Bretèche)
Proc. London Math. Soc. 108 (2014), 1030-1078. (arXiv:1210.4010)
50. Incomplete Kloosterman sums and multiplicative inverses in short intervals (with A. Haynes)
Int. J. Number Theory 9 (2013), 481-486. (arXiv:1204.6374)
49. Quadratic polynomials represented by norm forms (with D.R. Heath-Brown)
GAFA 22 (2012), 1124-1190. (arXiv:1109.0232)
48. Rational points on singular intersections of quadrics (with R. Munshi)

Compositio Math.

149

(arXiv:1108.1902)

47. Sums of three squareful numbers (with K. Van Valckenborgh)
Experimental Mathematics 21 (2012), 204-211. (arXiv:1106.4472)
46. Inhomogeneous quadratic congruences (with S. Baier)
Functiones et Approximatio 47 (2012), 267-286. (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), 551-576. (arXiv:1101.5464)
44. Inhomogeneous cubic congruences and rational points on del Pezzo surfaces (with S. Baier)
Journal reine angew. Math. 680 (2013), 69-151. (arXiv:1011.3434)
43. Power-free values of polynomials
Arch. Math. 96 (2011), 139-150.
42. Binary forms as sums of two squares and Châtelet surfaces (with R. de la Bretèche)
Israel J. Math. 191 (2012), 973-1012. (arXiv:1006.5859)
41. The divisor problem for binary cubic forms
J. Théorie Nombres Bordeaux 23 (2011), 579-602. (arXiv:1006.3476)
40. The Lang-Weil estimate for cubic hypersurfaces
Canad. Math. Bull. 56 (2013), 500-502.
39. On Manin's conjecture for a family of Châtelet surfaces (with R. de la Bretèche and E. Peyre)
Annals of Math. 175 (2012), 297-343. (arXiv:1002.0255)
38. The number of representations of rationals as a sum of unit fractions (with C. Elsholtz)
Illinois J. Math. 55 (2011), 685-696.
37. Least zero of a cubic form (with R. Dietmann and P.D.T.A. Elliott)
Math. Annalen 352 (2011), 745-778. (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), 41-50. (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), 1-69. (arXiv:0808.1616)
33. Le problème des diviseurs pour des formes binaires de degré 4 (with R. de la Bretèche)
Journal reine angew. Math. (arXiv:0808.2340) 646 (2010), 1-44.
32. Rational points on cubic hypersurfaces that split off a form
Compositio Math. 146 (2010), 853-885. (arXiv:0808.0125)
31. Manin's conjecture for a cubic surface with D_5 singularity (with U. Derenthal)
IMRN 14 (2009), 2620-2647. (arXiv:0807.4733)
30. Manin's conjecture for a quartic del Pezzo surface with A_4 singularity (with U. Derenthal)
Ann. Inst. Fourier 59 (2009), 1231-1265. (arXiv:0710.1560)
29. Recent progress on the quantitative arithmetic of del Pezzo surfaces
Proceedings of the 5th China-Japan Number Theory Conference (Osaka, 27-31 August 2008), World Scientific (2010), 1-19.
28. Solubility of Fermat equations (with R. Dietmann)
Quadratic forms - algebra, arithmetic and geometry, Contemporary Math. 493 (2009), 99-106. (arXiv:0805.3354)
27. Binary linear forms as sums of two squares (with R. de la Bretèche)
Compositio Math. 144 (2008), 1375-1402. (arXiv:1006.5859)
26. Rational points on quartic hypersurfaces (with D.R. Heath-Brown)
Journal reine angew. Math. 629 (2009), 37-88. (arXiv:math/0701348)
25. Integral points on cubic hypersurfaces (with D.R. Heath-Brown)
Analytic Number Theory: Essays in honour of Klaus Roth, CUP (2009), 75-90. (arXiv:math/0611086)
24. On the representation of integers by quadratic forms (with R. Dietmann)
Proc. London Math. Soc. 96 (2008), 389-416. (arXiv:math/0603358)
23. Counting rational points on cubic hypersurfaces
Mathematika 54 (2007), 93-112. (arXiv:0707.2296)
23a. Corrigendum for "Counting rational points on cubic hypersurfaces"
Mathematika 60 (2014), 101-107.
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), 579-605. (arXiv:math/0502510)
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), 39-56. (arXiv:math/0511041)
20. Density of integer solutions to diagonal quadratic forms.
Monatsh. Math. 152 (2007), 13-38. (arXiv:math/0603569)
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), 1-50. (arXiv:math/0509370)
18. Simultaneous equal sums of three powers (with D.R. Heath-Brown)
Proc. of the session on Diophantine geometry (Pisa, 1st April - 30th July, 2005), CRM series 4 (2007), 93-100. (arXiv:math/0509152)
17. On Manin's conjecture for singular del Pezzo surfaces of degree four, I (with R. de la Bretèche)
Michigan Math. J. 55 (2007), 51-80. (arXiv:math/0412086)
16. Sums of arithmetic functions over values of binary forms (with R. de la Bretèche)
Acta Arith. 125 (2006), 291-304. (arXiv:math/0604119)
15. The density of rational points on non-singular hypersurfaces, II (with D.R. Heath-Brown)
Proc. London Math. Soc. 93 (2006), 273-303. (arXiv:math/0505186)
14. The density of rational points on a certain singular cubic surface
J. Number Theory 119 (2006), 242-283.
13. The density of rational points on non-singular hypersurfaces, I (with D.R. Heath-Brown)
Bull. London Math. Soc. 38 (2006), 401-410. (arXiv:math/0502243)
12. Counting rational points on algebraic varieties (with D.R. Heath-Brown and P. Salberger)
Duke Math. J. 132 (2006), 545-578. (arXiv:math/0410117)
11. Equal sums of like polynomials
Bull. London Math. Soc. 37 (2005), 801-808. (arXiv:math/0507541)
10. Counting rational points on hypersurfaces (with D.R. Heath-Brown)
Journal reine angew. Math. 584 (2005), 83-115. (arXiv:math/0404456)
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. Heath-Brown)
Math. Zeit. 251 (2005), 233-247. (arXiv:math/0506497)
7. Equal sums of three powers (with D.R. Heath-Brown)
Invent. Math. 157 (2004), 553-573.
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), 385-395.
4. Counting rational points on cubic and quartic surfaces
Acta Arith. 108 (2003), 275-295.
3. A note on the distribution of rational points on threefolds
Quart. J. Math. 54 (2003), 33-39.
2. Counting rational points on diagonal quadratic surfaces
Quart. J. Math. 54 (2003), 11-31.
1. Equal sums of two kth powers
J. Number Theory 96 (2002), 293-318.

INDEX