Inventiones mathematicae

, Volume 170, Issue 1, pp 199–230 | Cite as

Cubic forms in 14 variables

Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baker, R.C.: Diagonal cubic equations II. Acta Arith. 53, 217–250 (1989)MATHMathSciNetGoogle Scholar
  2. 2.
    Balasubramanian, R.: An improvement on a theorem of Titchmarsh on the mean square of \(\big|\zeta\big(\frac{1}{2}+it\big)\big|\). Proc. Lond. Math. Soc., III. Ser. 36, 540–576 (1978)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Browning, T.D., Heath-Brown, D.R.: Counting rational points on hypersurfaces. J. Reine Angew. Math. 584, 83–115 (2005)MATHMathSciNetGoogle Scholar
  4. 4.
    Cassels, J.W.S., Guy, M.J.T.: On the Hasse principle for cubic surfaces. Mathematika 13, 111–120 (1966)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Davenport, H.: Cubic forms in sixteen variables. Proc. R. Soc. Lond., Ser. A 272, 285–303 (1963)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Davenport, H.: Analytic Methods for Diophantine Equations and Diophantine Inequalities. 2nd edn., Cambridge Mathematical Library. Cambridge University Press, Cambridge (2005)Google Scholar
  7. 7.
    Heath-Brown, D.R.: Mean value theorems for the Riemann Zeta-function. Théorie des Nombres, Sémin. Delange-Pisot-Poitou, Paris, 1979–80. Prog. Math. 12, 123–134 (1981)Google Scholar
  8. 8.
    Hooley, C.: On nonary cubic forms. J. Reine Angew. Math. 386, 32–98 (1988)MATHMathSciNetGoogle Scholar
  9. 9.
    Pleasants, P.A.B.: Cubic polynomials over algebraic number fields. J. Number Theory 7, 310–344 (1975)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Selmer, E.S.: The Diophantine equation a x 3+b y 3+c z 3=0. Acta Math. 85, 203–362 (1951)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Swinnerton-Dyer, H.P.F.: The solubility of diagonal cubic surfaces. Ann. Sci. Éc. Norm. Supér., IV. Sér. 34, 891–912 (2001)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematical InstituteOxfordUK

Personalised recommendations