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Cubic forms in 14 variables

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References

  1. Baker, R.C.: Diagonal cubic equations II. Acta Arith. 53, 217–250 (1989)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  3. Browning, T.D., Heath-Brown, D.R.: Counting rational points on hypersurfaces. J. Reine Angew. Math. 584, 83–115 (2005)

    MATH  MathSciNet  Google Scholar 

  4. Cassels, J.W.S., Guy, M.J.T.: On the Hasse principle for cubic surfaces. Mathematika 13, 111–120 (1966)

    Article  MathSciNet  Google Scholar 

  5. Davenport, H.: Cubic forms in sixteen variables. Proc. R. Soc. Lond., Ser. A 272, 285–303 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  6. Davenport, H.: Analytic Methods for Diophantine Equations and Diophantine Inequalities. 2nd edn., Cambridge Mathematical Library. Cambridge University Press, Cambridge (2005)

  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)

  8. Hooley, C.: On nonary cubic forms. J. Reine Angew. Math. 386, 32–98 (1988)

    MATH  MathSciNet  Google Scholar 

  9. Pleasants, P.A.B.: Cubic polynomials over algebraic number fields. J. Number Theory 7, 310–344 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  10. Selmer, E.S.: The Diophantine equation a x 3+b y 3+c z 3=0. Acta Math. 85, 203–362 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  11. Swinnerton-Dyer, H.P.F.: The solubility of diagonal cubic surfaces. Ann. Sci. Éc. Norm. Supér., IV. Sér. 34, 891–912 (2001)

    MATH  MathSciNet  Google Scholar 

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  1. Mathematical Institute, Oxford, 24–29, St. Giles’, OX1 3LB, UK

    D.R. Heath-Brown

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Heath-Brown, D. Cubic forms in 14 variables. Invent. math. 170, 199–230 (2007). https://doi.org/10.1007/s00222-007-0062-1

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