Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem: beyond Freĭman’s theorem. (English) Zbl 07808993 J. Lond. Math. Soc., II. Ser. 109, No. 1, Article ID e12820, 25 p. (2024). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, J. Lond. Math. Soc., II. Ser. 109, No. 1, Article ID e12820, 25 p. (2024; Zbl 07808993) Full Text: DOI arXiv OA License
Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem for larger powers. (English) Zbl 07771193 J. Reine Angew. Math. 805, 115-142 (2023). Reviewer: Mehdi Hassani (Zanjan) MSC: 11P05 11P55 11J71 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, J. Reine Angew. Math. 805, 115--142 (2023; Zbl 07771193) Full Text: DOI arXiv
Wooley, Trevor D. The paucity problem for certain symmetric Diophantine equations. (English) Zbl 07734851 Bull. Aust. Math. Soc. 108, No. 1, 29-39 (2023). MSC: 11D45 11D72 PDFBibTeX XMLCite \textit{T. D. Wooley}, Bull. Aust. Math. Soc. 108, No. 1, 29--39 (2023; Zbl 07734851) Full Text: DOI arXiv
Wooley, Trevor D. Subconvexity in the inhomogeneous cubic Vinogradov system. (English) Zbl 07731019 J. Lond. Math. Soc., II. Ser. 107, No. 2, 798-817 (2023). Reviewer: Giovanni Coppola (Napoli) MSC: 11P55 11L07 11D72 PDFBibTeX XMLCite \textit{T. D. Wooley}, J. Lond. Math. Soc., II. Ser. 107, No. 2, 798--817 (2023; Zbl 07731019) Full Text: DOI arXiv
Wooley, Trevor D. Paucity problems and some relatives of Vinogradov’s mean value theorem. (English) Zbl 07725807 Math. Proc. Camb. Philos. Soc. 175, No. 2, 327-343 (2023). MSC: 11D45 11P05 PDFBibTeX XMLCite \textit{T. D. Wooley}, Math. Proc. Camb. Philos. Soc. 175, No. 2, 327--343 (2023; Zbl 07725807) Full Text: DOI arXiv
Matomäki, Kaisa (ed.); Soundararajan, Kannan (ed.); Vaughan, Robert C. (ed.); Wooley, Trevor D. (ed.) Analytic number theory. Abstracts from the workshop held November 6–12, 2022. (English) Zbl 1521.00022 Oberwolfach Rep. 19, No. 4, 2895-2960 (2022). MSC: 00B05 00B25 11-06 11Bxx 11Dxx 11Jxx 11Pxx PDFBibTeX XMLCite \textit{K. Matomäki} (ed.) et al., Oberwolfach Rep. 19, No. 4, 2895--2960 (2022; Zbl 1521.00022) Full Text: DOI
Brüdern, Jörg; Wooley, Trevor D. A paucity problem for certain triples of diagonal equations. (English) Zbl 07729905 Bull. Lond. Math. Soc. 54, No. 4, 1396-1412 (2022). MSC: 11D45 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Bull. Lond. Math. Soc. 54, No. 4, 1396--1412 (2022; Zbl 07729905) Full Text: DOI arXiv
Brüdern, Jörg; Wooley, Trevor D. On smooth Weyl sums over biquadrates and Waring’s problem. (English) Zbl 1504.11103 Acta Arith. 204, No. 1, 19-40 (2022). Reviewer: Luis Gallardo (Brest) MSC: 11P05 11L15 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Acta Arith. 204, No. 1, 19--40 (2022; Zbl 1504.11103) Full Text: DOI arXiv
Brandes, Julia; Wooley, Trevor D. Optimal mean value estimates beyond Vinogradov’s mean value theorem. (English) Zbl 1497.11191 Acta Arith. 200, No. 2, 149-182 (2021). MSC: 11L15 11D45 11L07 11P55 PDFBibTeX XMLCite \textit{J. Brandes} and \textit{T. D. Wooley}, Acta Arith. 200, No. 2, 149--182 (2021; Zbl 1497.11191) Full Text: DOI arXiv
Brüdern, Jörg; Wooley, Trevor D. An instance where the major and minor arc integrals meet. (English) Zbl 1489.11053 Bull. Lond. Math. Soc. 51, No. 6, 1113-1128 (2019). Reviewer: Stephan Baier (Hāoṛā) MSC: 11D72 11P55 11L15 11L07 11E76 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Bull. Lond. Math. Soc. 51, No. 6, 1113--1128 (2019; Zbl 1489.11053) Full Text: DOI arXiv
Vaughan, Robert C.; Wooley, Trevor D. The asymptotic formula in Waring’s problem: higher order expansions. (English) Zbl 1415.11123 J. Reine Angew. Math. 742, 17-46 (2018). Reviewer: D. R. Heath-Brown (Garsington) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, J. Reine Angew. Math. 742, 17--46 (2018; Zbl 1415.11123) Full Text: DOI arXiv
Brandes, Julia; Wooley, Trevor D. Vinogradov systems with a slice off. (English) Zbl 1390.11099 Mathematika 63, No. 3, 797-817 (2017). Reviewer: Lajos Hajdu (Debrecen) MSC: 11L15 11D45 11L07 11P55 PDFBibTeX XMLCite \textit{J. Brandes} and \textit{T. D. Wooley}, Mathematika 63, No. 3, 797--817 (2017; Zbl 1390.11099) Full Text: DOI arXiv
Kumchev, Angel V.; Wooley, Trevor D. On the Waring-Goldbach problem for seventh and higher powers. (English) Zbl 1381.11099 Monatsh. Math. 183, No. 2, 303-310 (2017). Reviewer: Kaisa Matomäki (Turku) MSC: 11P32 11L20 11P05 11P55 PDFBibTeX XMLCite \textit{A. V. Kumchev} and \textit{T. D. Wooley}, Monatsh. Math. 183, No. 2, 303--310 (2017; Zbl 1381.11099) Full Text: DOI arXiv
Brüdern, Jörg; Wooley, Trevor D. Additive representation in short intervals. II: Sums of two like powers. (English) Zbl 1384.11095 Math. Z. 286, No. 1-2, 179-196 (2017). Reviewer: Mihály Szalay (Budapest) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Math. Z. 286, No. 1--2, 179--196 (2017; Zbl 1384.11095) Full Text: DOI arXiv
Wooley, Trevor D. Approximating the main conjecture in Vinogradov’s mean value theorem. (English) Zbl 1372.11086 Mathematika 63, No. 1, 292-350 (2017). Reviewer: Huaning Liu (Shaanxi) MSC: 11L15 11L07 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Mathematika 63, No. 1, 292--350 (2017; Zbl 1372.11086) Full Text: DOI arXiv
Kumchev, Angel V.; Wooley, Trevor D. On the Waring-Goldbach problem for eighth and higher powers. (English) Zbl 1358.11117 J. Lond. Math. Soc., II. Ser. 93, No. 3, 811-824 (2016). Reviewer: Mihály Szalay (Budapest) MSC: 11P32 11L20 11P05 11P55 PDFBibTeX XMLCite \textit{A. V. Kumchev} and \textit{T. D. Wooley}, J. Lond. Math. Soc., II. Ser. 93, No. 3, 811--824 (2016; Zbl 1358.11117) Full Text: DOI arXiv
Wooley, Trevor D. The cubic case of the main conjecture in Vinogradov’s mean value theorem. (English) Zbl 1365.11097 Adv. Math. 294, 532-561 (2016). Reviewer: Mehdi Hassani (Zanjan) MSC: 11L15 11L07 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Adv. Math. 294, 532--561 (2016; Zbl 1365.11097) Full Text: DOI arXiv
Brüdern, Jörg; Wooley, Trevor D. The Hasse principle for systems of diagonal cubic forms. (English) Zbl 1372.11048 Math. Ann. 364, No. 3-4, 1255-1274 (2016). Reviewer: Damaris Schindler (Utrecht) MSC: 11D72 11P55 11E76 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Math. Ann. 364, No. 3--4, 1255--1274 (2016; Zbl 1372.11048) Full Text: DOI arXiv
Keating, J. P.; Rudnick, Z.; Wooley, T. D. Number fields and function fields: coalescences, contrasts and emerging applications. (English) Zbl 1353.11098 Philos. Trans. A, R. Soc. Lond. 373, No. 2040, Article ID 20140315, 4 p. (2015). MSC: 11N05 11B05 94A60 PDFBibTeX XMLCite \textit{J. P. Keating} et al., Philos. Trans. A, R. Soc. Lond. 373, No. 2040, Article ID 20140315, 4 p. (2015; Zbl 1353.11098) Full Text: DOI
Wooley, Trevor D. Mean value estimates for odd cubic Weyl sums. (English) Zbl 1377.11090 Bull. Lond. Math. Soc. 47, No. 6, 946-957 (2015). MSC: 11L15 11L07 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Bull. Lond. Math. Soc. 47, No. 6, 946--957 (2015; Zbl 1377.11090) Full Text: DOI arXiv
Wei, Bin; Wooley, Trevor D. On sums of powers of almost equal primes. (English) Zbl 1338.11096 Proc. Lond. Math. Soc. (3) 111, No. 5, 1130-1162 (2015). Reviewer: Angel V. Kumchev (Towson) MSC: 11P32 11L07 11L20 11N05 11P05 11P55 PDFBibTeX XMLCite \textit{B. Wei} and \textit{T. D. Wooley}, Proc. Lond. Math. Soc. (3) 111, No. 5, 1130--1162 (2015; Zbl 1338.11096) Full Text: DOI arXiv
Wooley, Trevor D. Sums of three cubes. II. (English) Zbl 1408.11094 Acta Arith. 170, No. 1, 73-100 (2015). MSC: 11P05 11L15 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Acta Arith. 170, No. 1, 73--100 (2015; Zbl 1408.11094) Full Text: DOI arXiv
Wooley, Trevor D. Rational solutions of pairs of diagonal equations, one cubic and one quadratic. (English) Zbl 1333.11034 Proc. Lond. Math. Soc. (3) 110, No. 2, 325-356 (2015). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11D72 11L15 11P55 11D25 11D09 PDFBibTeX XMLCite \textit{T. D. Wooley}, Proc. Lond. Math. Soc. (3) 110, No. 2, 325--356 (2015; Zbl 1333.11034) Full Text: DOI arXiv
Friedlander, John B.; Wooley, Trevor D. On Waring’s problem: two squares and three biquadrates. (English) Zbl 1303.11111 Mathematika 60, No. 1, 153-165 (2014). Reviewer: L. N. Vaserstein (University Park) MSC: 11P05 PDFBibTeX XMLCite \textit{J. B. Friedlander} and \textit{T. D. Wooley}, Mathematika 60, No. 1, 153--165 (2014; Zbl 1303.11111) Full Text: DOI arXiv
Parsell, Scott T.; Prendiville, Sean M.; Wooley, Trevor D. Near-optimal mean value estimates for multidimensional Weyl sums. (English) Zbl 1320.11028 Geom. Funct. Anal. 23, No. 6, 1962-2024 (2013). Reviewer: Christian Elsholtz (Graz) MSC: 11D45 11P55 11D72 11L07 11L15 PDFBibTeX XMLCite \textit{S. T. Parsell} et al., Geom. Funct. Anal. 23, No. 6, 1962--2024 (2013; Zbl 1320.11028) Full Text: DOI arXiv
Wooley, Trevor D. Vinogradov’s mean value theorem via efficient congruencing. (English) Zbl 1267.11105 Ann. Math. (2) 175, No. 3, 1575-1627 (2012). Reviewer: Stephan Baier (Norwich) MSC: 11P05 11P55 11L07 PDFBibTeX XMLCite \textit{T. D. Wooley}, Ann. Math. (2) 175, No. 3, 1575--1627 (2012; Zbl 1267.11105) Full Text: DOI arXiv
Brüdern, J.; Wooley, T. D. The asymptotic formulae in Waring’s problem for cubes. (English) Zbl 1220.11126 J. Reine Angew. Math. 647, 1-23 (2010). Reviewer: Luis Gallardo (Brest) MSC: 11P05 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, J. Reine Angew. Math. 647, 1--23 (2010; Zbl 1220.11126) Full Text: DOI
Kawada, Koichi; Wooley, Trevor D. Davenport’s method and slim exceptional sets: the asymptotic formulae in Waring’s problem. (English) Zbl 1238.11091 Mathematika 56, No. 2, 305-321 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{K. Kawada} and \textit{T. D. Wooley}, Mathematika 56, No. 2, 305--321 (2010; Zbl 1238.11091) Full Text: DOI arXiv
Liu, Yu-Ru; Wooley, Trevor D. Waring’s problem in function fields. (English) Zbl 1221.11203 J. Reine Angew. Math. 638, 1-67 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11P05 11T55 11P55 PDFBibTeX XMLCite \textit{Y.-R. Liu} and \textit{T. D. Wooley}, J. Reine Angew. Math. 638, 1--67 (2010; Zbl 1221.11203) Full Text: DOI
Liu, Jianya; Wooley, Trevor D.; Yu, Gang The quadratic Waring-Goldbach problem. (English) Zbl 1056.11055 J. Number Theory 107, No. 2, 298-321 (2004). Reviewer: Koichi Kawada (Morioka) MSC: 11P32 11P05 11P55 PDFBibTeX XMLCite \textit{J. Liu} et al., J. Number Theory 107, No. 2, 298--321 (2004; Zbl 1056.11055) Full Text: DOI
Wooley, Trevor D. On Vu’s thin basis theorem in Waring’s problem. (English) Zbl 1047.11094 Duke Math. J. 120, No. 1, 1-34 (2003). Reviewer: George Greaves (Cardiff) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Duke Math. J. 120, No. 1, 1--34 (2003; Zbl 1047.11094) Full Text: DOI
Parsell, Scott T.; Wooley, Trevor D. A quasi-paucity problem. (English) Zbl 1027.11024 Mich. Math. J. 50, No. 3, 461-469 (2002). Reviewer: Roger Heath-Brown (Oxford) MSC: 11D45 11D72 PDFBibTeX XMLCite \textit{S. T. Parsell} and \textit{T. D. Wooley}, Mich. Math. J. 50, No. 3, 461--469 (2002; Zbl 1027.11024) Full Text: DOI
Laporta, M. B. S.; Wooley, T. D. The representation of almost all numbers as sums of unlike powers. (English) Zbl 1048.11074 J. Théor. Nombres Bordx. 13, No. 1, 227-240 (2001). Reviewer: Koichi Kawada (Morioka) MSC: 11P05 11P55 11L15 PDFBibTeX XMLCite \textit{M. B. S. Laporta} and \textit{T. D. Wooley}, J. Théor. Nombres Bordx. 13, No. 1, 227--240 (2001; Zbl 1048.11074) Full Text: DOI Numdam EuDML EMIS
Brüdern, Jörg; Wooley, Trevor D. On Waring’s problem: Three cubes and a sixth power. (English) Zbl 0989.11047 Nagoya Math. J. 163, 13-53 (2001). Reviewer: Roger Heath-Brown (Oxford) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{T. D. Wooley}, Nagoya Math. J. 163, 13--53 (2001; Zbl 0989.11047) Full Text: DOI
Brüdern, Jörg; Kawada, Koichi; Wooley, Trevor D. Additive representation in thin sequences. I: Waring’s problem for cubes. (English) Zbl 1020.11062 Ann. Sci. Éc. Norm. Supér. (4) 34, No. 4, 471-501 (2001). Reviewer: George Greaves (Cardiff) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{J. Brüdern} et al., Ann. Sci. Éc. Norm. Supér. (4) 34, No. 4, 471--501 (2001; Zbl 1020.11062) Full Text: DOI Numdam EuDML
Wooley, Trevor D. Sums of three cubes. (English) Zbl 1026.11075 Mathematika 47, No. 1-2, 53-61 (2000). Reviewer: George Greaves (Cardiff) MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Mathematika 47, No. 1--2, 53--61 (2000; Zbl 1026.11075) Full Text: DOI
Balog, A.; Brüdern, J.; Wooley, T. D. On smooth gaps between consecutive prime numbers. (English) Zbl 0967.11038 Mathematika 46, No. 1, 57-75 (1999). Reviewer: Peter Shiu (Loughborough) MSC: 11N05 11N36 PDFBibTeX XMLCite \textit{A. Balog} et al., Mathematika 46, No. 1, 57--75 (1999; Zbl 0967.11038) Full Text: DOI
Wooley, Trevor D. On Weyl’s inequality, Hua’s lemma, and exponential sums over binary forms. (English) Zbl 1130.11312 Duke Math. J. 100, No. 3, 373-423 (1999). Reviewer: Koichi Kawada (Morioka) (MR1719742) MSC: 11D72 11E76 11J71 11L07 11P55 PDFBibTeX XMLCite \textit{T. D. Wooley}, Duke Math. J. 100, No. 3, 373--423 (1999; Zbl 1130.11312) Full Text: DOI Euclid
Wooley, Trevor D. On simultaneous additive equations. IV. (English) Zbl 0994.11015 Mathematika 45, No. 2, 319-335 (1998). Reviewer: Koichi Kawada (Morioka) MSC: 11D72 11L15 11P55 11D25 PDFBibTeX XMLCite \textit{T. D. Wooley}, Mathematika 45, No. 2, 319--335 (1998; Zbl 0994.11015) Full Text: DOI
Vaughan, R. C.; Wooley, T. D. On a certain nonary cubic form and related equations. (English) Zbl 0847.11052 Duke Math. J. 80, No. 3, 669-735 (1995). Reviewer: G.Greaves (Cardiff) MSC: 11P05 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, Duke Math. J. 80, No. 3, 669--735 (1995; Zbl 0847.11052) Full Text: DOI
Montgomery, H. L.; Vaughan, R. C.; Wooley, T. D. Some remarks on Gauss sums associated with \(k\)th powers. (English) Zbl 0835.11032 Math. Proc. Camb. Philos. Soc. 118, No. 1, 21-33 (1995). Reviewer: D.R.Heath-Brown (Oxford) MSC: 11L05 11P05 PDFBibTeX XMLCite \textit{H. L. Montgomery} et al., Math. Proc. Camb. Philos. Soc. 118, No. 1, 21--33 (1995; Zbl 0835.11032) Full Text: DOI
Vaughan, Robert C.; Wooley, Trevor D. Further improvements in Waring’s problem. (English) Zbl 0849.11075 Acta Math. 174, No. 2, 147-240 (1995). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, Acta Math. 174, No. 2, 147--240 (1995; Zbl 0849.11075) Full Text: DOI
Vaughan, R. C.; Wooley, T. D. Further improvements in Waring’s problem. II: Sixth powers. (English) Zbl 0849.11076 Duke Math. J. 76, No. 3, 683-710 (1994). MSC: 11P05 11P55 PDFBibTeX XMLCite \textit{R. C. Vaughan} and \textit{T. D. Wooley}, Duke Math. J. 76, No. 3, 683--710 (1994; Zbl 0849.11076) Full Text: DOI