Rational points on nonsingular cubic hypersurfaces
Christopher M. Skinner
Source: Duke Math. J. Volume 75, Number 2
(1994), 409-466.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077287617
Mathematical Reviews number (MathSciNet): MR1290198
Zentralblatt MATH identifier: 0848.14009
Digital Object Identifier: doi:10.1215/S0012-7094-94-07512-1
References
[B1] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102–105.
Mathematical Reviews (MathSciNet): MR20:3828
Zentralblatt MATH: 0081.04501
Digital Object Identifier: doi:10.1112/S0025579300001145
[B2] 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
[B3] B. J. Birch, Waring's problem in algebraic number fields, Proc. Cambridge Philos. Soc. 57 (1961), 449–459.
Mathematical Reviews (MathSciNet): MR26:1306
Zentralblatt MATH: 0111.25104
Digital Object Identifier: doi:10.1017/S0305004100035490
[C] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957.
Mathematical Reviews (MathSciNet): MR19,396h
Zentralblatt MATH: 0077.04801
[CTS] J. Colliot-Thélène and P. Salberger, Arithmetic on some singular cubic hypersurfaces, Proc. London Math. Soc. (3) 58 (1989), no. 3, 519–549.
Mathematical Reviews (MathSciNet): MR90e:11091
Zentralblatt MATH: 0638.14011
Digital Object Identifier: doi:10.1112/plms/s3-58.3.519
[D1] 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
[D2] 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
[D3] 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
[De] P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. (1974), no. 43, 273–307.
Mathematical Reviews (MathSciNet): MR49:5013
Zentralblatt MATH: 0287.14001
Digital Object Identifier: doi:10.1007/BF02684373
[FM] C. Müller and W. Freeden, Multidimensional Euler and Poisson summation formulas, Resultate Math. 3 (1980), no. 1, 33–63.
Mathematical Reviews (MathSciNet): MR82d:10071
Zentralblatt MATH: 0461.40004
[HW] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954.
Mathematical Reviews (MathSciNet): MR16,673c
Zentralblatt MATH: 0058.03301
[HB] 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
[H1] C. Hooley, On nonary cubic forms I, 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
[H2] C. 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
[K] H. D. Kloosterman, On the representation of numbers in the form $ax^2+by^2+cz^2+dt^2$, Acta Math. 49 (1926), 407–464.
[La] S. Lang, Algebraic number theory, Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR95f:11085
Zentralblatt MATH: 0601.12001
[L] D. J. Lewis, Cubic forms over algebraic number fields, Mathematika 4 (1957), 97–101.
Mathematical Reviews (MathSciNet): MR20:3827
Zentralblatt MATH: 0081.04403
Digital Object Identifier: doi:10.1112/S0025579300001133
[PW] A. Pethö and B. M. M. de Weger, Products of prime powers in binary recurrence sequences. I. The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comp. 47 (1986), no. 176, 713–727.
Mathematical Reviews (MathSciNet): MR87m:11027a
Zentralblatt MATH: 0623.10011
Digital Object Identifier: doi:10.2307/2008185
JSTOR: links.jstor.org
[P] P. A. B. Pleasants, Cubic polynomials over algebraic number fields, J. Number Theory 7 (1975), no. 3, 310–344.
Mathematical Reviews (MathSciNet): MR56:11895
Zentralblatt MATH: 0328.12003
Digital Object Identifier: doi:10.1016/0022-314X(75)90024-4
[Ra] C. P. Ramanujam, Cubic forms over algebraic number fields, Proc. Cambridge Philos. Soc. 59 (1963), 683–705.
Mathematical Reviews (MathSciNet): MR27:4793
Zentralblatt MATH: 0129.02701
Digital Object Identifier: doi:10.1017/S0305004100003698
[Ry] C. Ryavec, Cubic forms over algebraic number fields, Proc. Cambridge Philos. Soc. 66 (1969), 323–333.
Mathematical Reviews (MathSciNet): MR39:5470
Zentralblatt MATH: 0222.10024
Digital Object Identifier: doi:10.1017/S0305004100045011
[S] W. 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
[T] W. Tartakowski, Über Asymptotische Gesetze der “Algemeinen” Diophantischen, Bull. Acad. Sci. USSR (1935), 483–524.
[V] R. C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981.
Mathematical Reviews (MathSciNet): MR84b:10002
Zentralblatt MATH: 0455.10034
Duke Mathematical Journal
