On Weyl’s inequality, Hua’s lemma, and exponential sums over binary forms

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On Weyl’s inequality, Hua’s lemma, and exponential sums over binary forms

Trevor D. Wooley

Source: Duke Math. J. Volume 100, Number 3 (1999), 373-423.

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Primary Subjects: 11D72

Secondary Subjects: 11E76, 11J71, 11L07, 11P55

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227493
Mathematical Reviews number (MathSciNet): MR1719742
Zentralblatt MATH identifier: 01425261
Digital Object Identifier: doi:10.1215/S0012-7094-99-10014-7

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References

[1] G. I. Arkhipov and A. A. Karatsuba, A multidimensional analogue of the Waring problem, Dokl. Akad. Nauk SSSR 295 (1987), no. 3, 521–523, (in Russian).

Mathematical Reviews (MathSciNet): MR88j:11013

Zentralblatt MATH: 0655.10043

[2] G. I. Arkhipov, A. A. Karatsuba, and V. N. Chubarikov, Teoriya kratnykh trigonometricheskikh summ, “Nauka”, Moscow, 1987.

Mathematical Reviews (MathSciNet): MR89h:11050

Zentralblatt MATH: 0638.10037

[3] R. C. Baker, Diophantine inequalities, London Mathematical Society Monographs. New Series, vol. 1, The Clarendon Press Oxford University Press, New York, 1986.

Mathematical Reviews (MathSciNet): MR88f:11021

Zentralblatt MATH: 0592.10029

[4] B. J. Birch, Forms in many variables, Proc. Roy. Soc. Ser. A 265 (1961/1962), 245–263.

Mathematical Reviews (MathSciNet): MR27:132

Zentralblatt MATH: 0103.03102

[5] B. J. Birch and H. Davenport, Note on Weyl's inequality, Acta Arith. 7 (1961/1962), 273–277.

Mathematical Reviews (MathSciNet): MR25:1132

Zentralblatt MATH: 0105.03801

[6] K. D. Boklan and T. D. Wooley, On Weyl sums for smaller exponents, in preparation.

[7] E. Bombieri and J. Pila, The number of integral points on arcs and ovals, Duke Math. J. 59 (1989), no. 2, 337–357.

Mathematical Reviews (MathSciNet): MR90j:11099

Zentralblatt MATH: 0718.11048

Digital Object Identifier: doi:10.1215/S0012-7094-89-05915-2

Project Euclid: euclid.dmj/1077308005

[8] E. Bombieri and W. M. Schmidt, On Thue's equation, Invent. Math. 88 (1987), no. 1, 69–81.

Mathematical Reviews (MathSciNet): MR88d:11026

Zentralblatt MATH: 0614.10018

Digital Object Identifier: doi:10.1007/BF01405092

[9] Jörg Brüdern and Trevor D. Wooley, The addition of binary cubic forms, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 356 (1998), no. 1738, 701–737.

Mathematical Reviews (MathSciNet): MR99e:11128

Zentralblatt MATH: 0909.11043

Digital Object Identifier: doi:10.1098/rsta.1998.0182

JSTOR: links.jstor.org

[10] S. Chowla and H. Davenport, On Weyl's inequality and Waring's problem for cubes, Acta Arith. 6 (1960/1961), 505–521.

Mathematical Reviews (MathSciNet): MR24:A102

Zentralblatt MATH: 0163.04101

[11] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London. Ser. A 251 (1959), 193–232.

Mathematical Reviews (MathSciNet): MR21:4136

Zentralblatt MATH: 0084.27202

Digital Object Identifier: doi:10.1098/rsta.1959.0002

JSTOR: links.jstor.org

[12] H. Davenport, Analytic methods for Diophantine equations and Diophantine inequalities, The University of Michigan, Fall Semester, vol. 1962, Ann Arbor Publishers, Ann Arbor, Mich., 1963.

Mathematical Reviews (MathSciNet): MR28:3002

[13] H. Davenport, Cubic forms in $29$ variables, Proc. Roy. Soc. Ser. A 266 (1962), 287–298.

Mathematical Reviews (MathSciNet): MR25:50

Zentralblatt MATH: 0103.03101

Digital Object Identifier: doi:10.1098/rspa.1962.0062

[14] H. Davenport, Cubic forms in sixteen variables, Proc. Roy. Soc. Ser. A 272 (1963), 285–303.

Mathematical Reviews (MathSciNet): MR27:5734

Zentralblatt MATH: 0107.04102

Digital Object Identifier: doi:10.1098/rspa.1963.0054

[15] H. Davenport and H. Heilbronn, On Waring's problem: Two cubes and one square, Proc. London Math. Soc. (2) 43 (1937), 73–104.

[16] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Roy. Soc. Ser. A 274 (1963), 443–460.

Mathematical Reviews (MathSciNet): MR27:3617

Zentralblatt MATH: 0118.28002

Digital Object Identifier: doi:10.1098/rspa.1963.0143

[17] T. Estermann, Einige Sätze über quadratfrei Zahlen, Math. Ann. 105 (1931), 653–662.

[18] Kevin B. Ford, New estimates for mean values of Weyl sums, Internat. Math. Res. Notices (1995), no. 3, 155–171 (electronic).

Mathematical Reviews (MathSciNet): MR96a:11101

Zentralblatt MATH: 0821.11050

Digital Object Identifier: doi:10.1155/S1073792895000122

[19] Glyn Harman, Trigonometric sums over primes. I, Mathematika 28 (1981), no. 2, 249–254 (1982).

Mathematical Reviews (MathSciNet): MR83j:10045

Zentralblatt MATH: 0465.10029

Digital Object Identifier: doi:10.1112/S0025579300010305

[20] D. R. Heath-Brown, Cubic forms in ten variables, Proc. London Math. Soc. (3) 47 (1983), no. 2, 225–257.

Mathematical Reviews (MathSciNet): MR85b:11025

Zentralblatt MATH: 0494.10012

Digital Object Identifier: doi:10.1112/plms/s3-47.2.225

[21] Christopher Hooley, On nonary cubic forms, J. Reine Angew. Math. 386 (1988), 32–98.

Mathematical Reviews (MathSciNet): MR89h:11014

Zentralblatt MATH: 0641.10019

Digital Object Identifier: doi:10.1515/crll.1988.386.32

[22] Christopher Hooley, On nonary cubic forms. II, J. Reine Angew. Math. 415 (1991), 95–165.

Mathematical Reviews (MathSciNet): MR92b:11017

Zentralblatt MATH: 0719.11017

Digital Object Identifier: doi:10.1515/crll.1991.415.95

[23] Christopher Hooley, On nonary cubic forms. III, J. Reine Angew. Math. 456 (1994), 53–63.

Mathematical Reviews (MathSciNet): MR95i:11026

Zentralblatt MATH: 0833.11048

Digital Object Identifier: doi:10.1515/crll.1994.456.53

[24] D. J. Lewis, Diophantine problems: solved and unsolved, Number theory and applications (Banff, AB, 1988) ed. R. A. Mollin, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 265, Kluwer Acad. Publ., Dordrecht, 1989, pp. 103–121.

Mathematical Reviews (MathSciNet): MR92f:11054

Zentralblatt MATH: 0685.10001

[25] Wolfgang M. Schmidt, The density of integer points on homogeneous varieties, Acta Math. 154 (1985), no. 3-4, 243–296.

Mathematical Reviews (MathSciNet): MR86h:11027

Zentralblatt MATH: 0561.10010

Digital Object Identifier: doi:10.1007/BF02392473

[26] W. Tartakovsky, Über asymptotische Gesetze der allgemeinen Diophantischen Analyse mit vielen Unbekannten, Bull. Acad. Sci. USSR (1935), 483–524.

[27] R. C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts in Mathematics, vol. 125, Cambridge University Press, Cambridge, 1997, second edition.

Mathematical Reviews (MathSciNet): MR98a:11133

Zentralblatt MATH: 0868.11046

[28] Robert C. Vaughan and Trevor D. Wooley, Further improvements in Waring's problem, Acta Math. 174 (1995), no. 2, 147–240.

Mathematical Reviews (MathSciNet): MR96j:11129a

Zentralblatt MATH: 0849.11075

Digital Object Identifier: doi:10.1007/BF02392467

[29] Trevor D. Wooley, On Vinogradov's mean value theorem, Mathematika 39 (1992), no. 2, 379–399.

Mathematical Reviews (MathSciNet): MR94d:11074

Zentralblatt MATH: 0769.11036

Digital Object Identifier: doi:10.1112/S0025579300015102

[30] Trevor D. Wooley, Quasi-diagonal behaviour in certain mean value theorems of additive number theory, J. Amer. Math. Soc. 7 (1994), no. 1, 221–245.

Mathematical Reviews (MathSciNet): MR94j:11076

Zentralblatt MATH: 0786.11053

Digital Object Identifier: doi:10.2307/2152728

JSTOR: links.jstor.org

[31] Trevor D. Wooley, New estimates for Weyl sums, Quart. J. Math. Oxford Ser. (2) 46 (1995), no. 181, 119–127.

Mathematical Reviews (MathSciNet): MR95m:11110

Zentralblatt MATH: 0855.11043

Digital Object Identifier: doi:10.1093/qmath/46.1.119

[32] Trevor D. Wooley, New estimates for smooth Weyl sums, J. London Math. Soc. (2) 51 (1995), no. 1, 1–13.

Mathematical Reviews (MathSciNet): MR96e:11109

Zentralblatt MATH: 0833.11041

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