1990
[1] T. D. Wooley, On simultaneous additive equations, III, Mathematika 37 (1990), 85-96
1991
[2] T. D. Wooley, On simultaneous additive equations, I, Proc. London Math. Soc. (3) 63 (1991), 1-34
[3] T. D. Wooley, On simultaneous additive equations, II, J. Reine Angew. Math. 419 (1991), 141-198
[4] R. C. Vaughan and T. D. Wooley, On a problem related to one of Littlewood and Offord, Quart. J. Math. Oxford (2) 42 (1991), 379-386
[5] R. C. Vaughan and T. D. Wooley, Waring's problem: some refinements, Proc. London Math. Soc. (3) 63 (1991), 35-68
1992
[6] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164
[7] T. D. Wooley, On Vinogradov's mean value theorem, Mathematika 39 (1992), 379-399
Corrigendum: ``On Vinogradov's mean value theorem'', Mathematika 40 (1993), 152
1993
[8] T. D. Wooley, On Vinogradov's mean value theorem, II, Michigan Math. J. 40 (1993), 681-686
[9] T. D. Wooley, A note on symmetric diagonal equations, Number Theory with an emphasis on the Markoff spectrum (Provo, UT, 1991), Editors: A. D. Pollington and W. Moran, Dekker, New York, 1993, pp 317-321
[10] T. D. Wooley, The application of a new mean value theorem to the fractional parts of polynomials, Acta Arith. 65 (1993), 163-179
[11] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, III: eighth powers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), 385-396
1994
[12] T. D. Wooley, Quasi-diagonal behaviour in certain mean value theorems of additive number theory, J. Amer. Math. Soc. 7 (1994), 221-245
[13] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, II: sixth powers, Duke Math. J. 76 (1994), 683-710
1995
[14] T. D. Wooley, New estimates for smooth Weyl sums, J. London Math. Soc. 51 (1995), 1-13
[15] T. D. Wooley, New estimates for Weyl sums, Quart. J. Math. Oxford (2) 46 (1995), 119-127
[16] T. D. Wooley, Sums of two cubes, Internat. Math. Res. Notices (1995), 181-185
[17] C. M. Skinner and T. D. Wooley, Sums of two kth powers, J. Reine Angew. Math. 462 (1995), 57-68
[18] H. L. Montgomery, R. C. Vaughan and T. D. Wooley, Some remarks on Gauss sums associated with kth powers, Math. Proc. Cambridge Philos. Soc. 118 (1995), 21-33
[19] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, Acta Math. 174 (1995), 147-240
[20] T. D. Wooley, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour, Invent. Math. 122 (1995), 421-451
[21] R. C. Vaughan and T. D. Wooley, On a certain nonary cubic form and related equations, Duke Math. J. 80 (1995), 669-735
[22] R. C. Baker, J. Bruedern and T. D. Wooley, Cubic diophantine inequalities, Mathematika 42 (1995), 264-277
1996
[23] T. D. Wooley, An affine slicing approach to certain paucity problems, Analytic Number Theory: Proceedings of a Conference in Honor of Heini Halberstam (B. C. Berndt, H. G. Diamond and A. J. Hildebrand, eds.), vol. 2, 1996, pp. 803-815.
[24] T. D. Wooley, A note on simultaneous congruences, J. Number Theory 58 (1996), 288-297
[25] T. D. Wooley, Some remarks on Vinogradov's mean value theorem and Tarry's problem, Monatsh. Math. 122 (1996), 265-273
1997
[26] R. C. Vaughan and T. D. Wooley, A special case of Vinogradov's mean value theorem, Acta Arith. 79 (1997), 193-204
[27] C. M. Skinner and T. D. Wooley, On the paucity of non-diagonal solutions in certain diagonal Diophantine systems, Quart. J. Math. Oxford (2) 48 (1997), 255-277
[28] T. D. Wooley, On exponential sums over smooth numbers, J. Reine Angew. Math. 488 (1997), 79-140
[29] T. D. Wooley, Linear spaces on cubic hypersurfaces, and pairs of cubic homogeneous equations, Bull. London Math. Soc. 29 (1997), 556-562
[30] T. D. Wooley, Forms in many variables, Analytic Number Theory: Proceedings of the 39th Taniguchi International Symposium, Kyoto, May 1996 (Y. Motohashi, ed.), London Mathematical Society Lecture Notes 247, Cambridge University Press, Cambridge, 1997, pp. 361-376
1998
[31] M. A. Bennett, N. P. Dummigan and T. D. Wooley, The representation of integers by binary additive forms, Compositio Math. 111 (1998), 15-33
[32] T. D. Wooley, On the local solubility of diophantine systems, Compositio Math. 111 (1998), 149-165
[33] R. C. Vaughan and T. D. Wooley, On the distribution of generating functions, Bull. London Math. Soc. 30 (1998), 113-122
[34] J. Bruedern and T. D. Wooley, The addition of binary cubic forms, Philos. Trans. Roy. Soc. London Ser. A 356 (1998), 701-737
[35] J. Bruedern, A. Granville, A. Perelli, R. C. Vaughan and T. D. Wooley, On the exponential sum over k-free numbers, Philos. Trans. Roy. Soc. London Ser. A 356 (1998), 739-761
[36] A. Balog and T. D. Wooley, On strings of consecutive integers with no large prime factors, J. Austral. Math. Soc. Ser. A 64 (1998), 266-276
[37] T. D. Wooley, An explicit version of Birch's Theorem, Acta Arith. 85 (1998), 79-96
[38] M. Kuehleitner, W. G. Nowak, J. Schoissengeier and T. Wooley, On sums of two cubes: an $\Omega_+$-estimate for the error term, Acta Arith. 85 (1998), 179-195
[39] K. Kawada and T. D. Wooley, Sums of fifth powers and related topics, Acta Arith. 87 (1998), 27-65
[40] T. D. Wooley, On simultaneous additive equations, IV, Mathematika 45 (1998), 319-335
1999
[41] W. Y. Tsui and T. D. Wooley, The paucity problem for simultaneous quadratic and biquadratic equations, Math. Proc. Cambridge Philos. Soc. 126 (1999), 209-221.
[42] T. D. Wooley, Diophantine problems in many variables: the role of additive number theory, S. D. Ahlgren et al. (eds.), Topics in Number Theory, Kluwer Academic Publishers, 1999, pp. 49-83.
[43] K. Kawada and T. D. Wooley, Sums of fourth powers and related topics, J. Reine Angew. Math. 512 (1999), 173-223.
[44] J. Bruedern and T. D. Wooley, On Waring's problem: a square, four cubes and a biquadrate, Math. Proc. Cambridge Philos. Soc. 127 (1999), 193-200.
[45] T. D. Wooley, On Weyl's inequality, Hua's Lemma, and exponential sums over binary forms, Duke Math. J. 100 (1999), 373-423.
[46] A. Balog, J. Bruedern and T. D. Wooley, On smooth gaps between consecutive prime numbers, Mathematika 46 (1999), 57-75.
2000
[47] T. D. Wooley, Sums and differences of two cubic polynomials, Monatsh. Math. 129 (2000), 159-169.
[48] J. Bruedern, A. Perelli and T. D. Wooley, Twins of k-free numbers and their exponential sum, Michigan Math. J. 47 (2000), 173-190.
[49] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's Problem, IV: higher powers, Acta Arith. 94 (2000), 203-285.
[50] T. D. Wooley, Quasi-diagonal behaviour and smooth Weyl sums, Monatsh. Math. 130 (2000), 161-170.
[51] A. Balog and T. D. Wooley, Sums of two squares in short intervals, Canad. J. Math. 52 (2000), 673-694.
[52] T. D. Wooley, Weyl's inequality and exponential sums over binary forms, Funct. Approx. Comment. Math. 28 (2000), 83--95.
[53] J. Bruedern and T. D. Wooley, On Waring's problem: two cubes and seven biquadrates, Tsukuba J. Math. 24 (2000), 387--417.
[54] T. D. Wooley, Sums of three cubes, Mathematika 47 (2000), 53--61.
[55] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, II: the binary Goldbach problem, Mathematika 47 (2000), 117--125.
2001
[56] J. Bruedern and T. D. Wooley, On Waring's problem for cubes and smooth Weyl sums, Proc. London Math. Soc. (3) 82 (2001), 89--109.
[57] K. Kawada and T. D. Wooley, On the Waring-Goldbach problem for fourth and fifth powers, Proc. London Math. Soc. (3) 83 (2001), 1--50.
[58] M. B. S. Laporta and T. D. Wooley, The representation of almost all numbers as sums of unlike powers, J. Theor. Nombres Bordeaux 13 (2001), 227--240.
[59] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, I: Waring's problem for cubes, Ann. Sci. École Norm. Sup. (4) 34 (2001), 471--501.
[60] J. Bruedern and T. D. Wooley, On Waring's problem: three cubes and a sixth power, Nagoya Math. J. 163 (2001), 13--53.
[61] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, III: asymptotic formulae, Acta Arith. 100 (2001), 267--289.
[62] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, IV: lower bound methods, Quart. J. Math. Oxford (2) 52 (2001), 423--436.
[63] T. D. Wooley, Hua's lemma and exponential sums over binary forms, in: "Rational points on algebraic varieties", Progr. Math., vol. 199, Birkhauser, Boston, Boston, MA, 2001, pp. 405--446.
2002
[64] S. T. Parsell and T. D. Wooley, On pairs of diagonal quintic forms, Compositio Math. 131 (2002), 61--96.
[65] T. D. Wooley, Slim exceptional sets for sums of cubes, Canad. J. Math. 54 (2002), 417--448.
[66] T. D. Wooley, Slim exceptional sets in Waring's problem: one square and five cubes, Quart. J. Math. 53 (2002), 111--118.
[67] T. D. Wooley, Slim exceptional sets for sums of four squares, Proc. London Math. Soc. (3) 85 (2002), 1--21.
[68] K. Kawada and T. D. Wooley, Slim exceptional sets for sums of fourth and fifth powers, Acta Arith. 103 (2002), 225--248.
[69] J. Bruedern and T. D. Wooley, Hua's lemma and simultaneous diagonal equations, Bull. London Math. Soc. 34 (2002), 279--283.
[70] T. D. Wooley, Diophantine methods for exponential sums, and exponential sums for diophantine problems, Proceedings of the International Congress of Mathematicians, August 20--28, 2002, Beijing, Volume II, Higher Education Press, 2002, pp. 207--217.
[71] R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, in: Number Theory for the Millenium, Vol. III (Bennett et al., eds.), A. K. Peters, 2002, pp. 301--340.
[72] S. T. Parsell and T. D. Wooley, A quasi-paucity problem, Michigan Math. J. 50 (2002), 461--469.
[73] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VI: representing primes, and related problems, Glasg. Math. J. 44 (2002), 419--434.
2003
[74] T. D. Wooley, On the difficulty of the local solubility problem for additive equations, Acta Arith. 107 (2003), 127--156.
[75] J. Bruedern and T. D. Wooley, The paucity problem for certain pairs of diagonal equations, Quart. J. Math. 54 (2003), 41--48.
[76] T. D. Wooley, Slim exceptional sets and the asymptotic formula in Waring's problem, Math. Proc. Cambridge Philos. Soc. 134 (2003), 193--206.
[77] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, V: mixed problems of Waring's type, Math. Scand. 92 (2003), 181--209.
[78] R. Dietmann and T. D. Wooley, Pairs of cubic forms in many variables, Acta Arith 110 (2003), 125--140.
[79] T. D. Wooley, On Vu's thin basis theorem in Waring's problem, Duke Math. J. 120 (2003), 1--34.
[80] T. D. Wooley, On diophantine inequalities: Freeman's asymptotic formulae, Proceedings of the Session in analytic number theory and Diophantine equations (Bonn, January -- June, 2002), Bonn 2003, Edited by D. R. Heath-Brown and B. Z. Moroz, Bonner Mathematische Schriften, Nr. 360, Article 30, 32pp.
2004
[81] T. D. Wooley, A light-weight version of Waring's problem, J. Austral. Math. Soc. 76 (2004), 303--316.
[82] J. Bruedern and T. D. Wooley, Asymptotic formulae for pairs of diagonal equations, Math. Proc. Cambridge Philos. Soc. 137 (2004), 227--235.
[83] Jianya Liu, T. D. Wooley and Gang Yu, The quadratic Waring-Goldbach problem, J. Number Theory 107 (2004), 298--321.
[84] J. Bruedern and T. D. Wooley, Additive representation in short intervals, I: Waring's problem for cubes, Compositio Math. 140 (2004), 1197--1220.
2005
[85] J.-M. Deshouillers, K. Kawada and T. D. Wooley, On sums of sixteen biquadrates, Mem. Soc. Math. Fr. (N.S.) No. 100 (2005), vi+120pp.
2007
[86] J. Bruedern and T. D. Wooley, The density of integral solutions for pairs of diagonal cubic equations, Clay Math. Proceedings 7 (2007), 57--76.
[87] Yu-Ru Liu and T. D. Wooley, The unrestricted variant of Waring's problem in function fields, Funct. Approx. Comment. Math. 37 (2007), 285--292.
[88] J. Bruedern and T. D. Wooley, The Hasse principle for pairs of diagonal cubic forms, Annals of Math. 166 (2007), 865--895.
2008
[89] T. D. Wooley, Artin's Conjecture for septic and unidecic forms, Acta Arith. 133 (2008), 25--35.
[90] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VII: restricted moments of the number of representations, Tsukuba J. Math. 32 (2008), 383--406.
2009
[91] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VIII: Diophantine inequalities in review, Number Theory. Dreaming in Dreams, Proceedings of the 5th China-Japan Seminar, Higashi-Osaka, Japan, 27-31 August 2008, eds. T. Aoki, S. Kanemitsu and J. Y. Liu, World Scientific, 2009, pp. 20--79.
2010
[92] J. Bruedern, R. Dietmann, J. Y. Liu and T. D. Wooley, A Birch-Goldbach theorem, Arch. Math. (Basel) 94 (2010), 53--58.
[93] Yu-Ru Liu and T. D. Wooley, Waring's problem in function fields, J. Reine Angew. Math. 638 (2010), 1--67.
[94] T. D. Wooley, A note on simultaneous congruences, II: Mordell revised, J. Austral Math. Soc. 88 (2010), 261--275.
[95] K. Kawada and T. D. Wooley, Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem, Mathematika 56 (2010), 305--321.
[96] P. Salberger and T. D. Wooley, Rational points on complete intersections of higher degree, and mean values of Weyl sums, J. London Math. Soc. (2) 82 (2010), 317--342.
[97] K. Kawada and T. D. Wooley, Relations between exceptional sets for additive problems, J. London Math. Soc. (2) 82 (2010), 437--458.
[98] J. Bruedern and T. D. Wooley, The asymptotic formulae in Waring's problem for cubes, J. Reine Angew. Math. 647 (2010), 1--23.
[99] J. Bruedern and T. D. Wooley, On Waring's problem: three cubes and a minicube, Nagoya Math. J. 200 (2010), 59--91.
2011
[100] J. Bruedern and T. D. Wooley, Asymptotic formulae for pairs of diagonal cubic equations, Canad. J. Math. 63 (2011), 38--54.
[101] J. Bruedern and T. D. Wooley, Sparse variance for primes in arithmetic progression, Quart. J. Math. 62 (2011), 289--305.
[102] Y. Dodis, X. Li, T. D. Wooley and D. Zuckerman, Privacy amplification and non-malleable extractors via character sums, Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2011), 668--677.
2012
[103] K. D. Boklan and T. D. Wooley, On Weyl sums for smaller exponents, Funct. Approx. Comment. Math. 46 (2012), 91--107.
[104] T. D. Wooley, The asymptotic formula in Waring's problem, Internat. Math. Res. Notices (2012), No. 7, 1485--1504.
[105] T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, Annals of Math. 175 (2012), 1575--1627.
[106] C. V. Spencer and T. D. Wooley, Diophantine inequalities and quasi-algebraically closed fields, Israel J. Math. 191 (2012), 721--738.
[107] T. D. Wooley and T. D. Ziegler, Multiple recurrence and convergence along the primes, Amer. J. Math. 134 (2012), 1705--1732.
In press
[108] J. Bruedern, K. Kawada and T. D. Wooley, Annexe to the gallery: an addendum to "Additive representation in thin sequences, VIII: Diophantine inequalities in review", Proceedings of the 6th China-Japan Seminar (in press), 6pp.
[109] T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, II, Duke Math. J. (in press), 58pp.
[110] J. Bruedern and T. D. Wooley, Subconvexity for additive equations: pairs of undenary cubic forms, J. Reine Angew. Math. (in press), 37pp.
[111] T. D. Wooley, On Waring's problem: two squares, two cubes and two sixth powers, Quart J. Math. (in press), 13pp.
Accepted
[112] J. B. Friedlander and T. D. Wooley, On Waring's problem: two squares and three biquadrates, Mathematika (accepted, to appear), 13pp.
[113] S. T. Parsell and T. D. Wooley, Exceptional sets for Diophantine inequalities, Internat. Math. Res. Notices (accepted, to appear), 43pp.
[114] S. T. Parsell, S. M. Prendiville and T. D. Wooley, Near-optimal mean value estimates for multidimensional Weyl sums, Geom. Funct. Anal. (accepted, to appear), 58pp.
Submitted
[115] Y. Dodis, X. Li, T. D. Wooley and D. Zuckerman, Privacy amplification and non-malleable extractors via character sums, full version, submitted, 30pp.
[116] T. D. Wooley, On Waring's problem: some consequences of Golubeva's method, submitted, 19pp.
[117] T. D. Wooley, On Linnik's conjecture: sums of squares and microsquares, submitted, 18pp.
Preprints and papers in preparation
[118] T. D. Wooley, On the local solubility problem for simultaneous additive equations.