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Volumn 79, Issue 2, 1999, Pages 241-259

The solubility of diagonal cubic Diophantine equations

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EID: 0040916926     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611599011946     Document Type: Article
Times cited : (7)

References (22)
  • 1
    • 0011330430 scopus 로고
    • Diagonal cubic equations, II
    • R. C. BAKER, 'Diagonal cubic equations, II', Acta Arith. 53 (1989) 217-250.
    • (1989) Acta Arith. , vol.53 , pp. 217-250
    • Baker, R.C.1
  • 2
    • 0001081335 scopus 로고
    • The average rank of elliptic curves, I
    • A. BRUMER, 'The average rank of elliptic curves, I', Invent. Math. 109 (1992) 445-472.
    • (1992) Invent. Math. , vol.109 , pp. 445-472
    • Brumer, A.1
  • 3
    • 84941463730 scopus 로고
    • Arithmetic on curves of genus 1. I. On a conjecture of Selmer
    • J. W. S. CASSELS, 'Arithmetic on curves of genus 1. I. On a conjecture of Selmer', J. Reine Angew. Math. 202 (1959) 52-99.
    • (1959) J. Reine Angew. Math. , vol.202 , pp. 52-99
    • Cassels, J.W.S.1
  • 4
    • 84941504750 scopus 로고
    • Arithmetic on curves of genus 1. IV. Proof of the Hauptvermutung
    • J. W. S. CASSELS, 'Arithmetic on curves of genus 1. IV. Proof of the Hauptvermutung', J. Reine Angew. Math. 211 (1962) 95-112.
    • (1962) J. Reine Angew. Math. , vol.211 , pp. 95-112
    • Cassels, J.W.S.1
  • 5
    • 84974122244 scopus 로고
    • On the Hasse principle for cubic surfaces
    • J. W. S. CASSELS and M. J. T. GUY, 'On the Hasse principle for cubic surfaces', Mathematika 13 (1966) 111-120.
    • (1966) Mathematika , vol.13 , pp. 111-120
    • Cassels, J.W.S.1    Guy, M.J.T.2
  • 6
    • 0011575677 scopus 로고
    • Sur le principe de Hasse et l'approximation faible, et sur une hypothèse de Schinzel
    • J.-L. COLLIOT-THÉLÈNE and J.-J. SANSUC, 'Sur le principe de Hasse et l'approximation faible, et sur une hypothèse de Schinzel', Acta Arith. 41 (1982) 33-53.
    • (1982) Acta Arith. , vol.41 , pp. 33-53
    • Colliot-Thélène, J.-L.1    Sansuc, J.-J.2
  • 7
    • 0040142412 scopus 로고
    • Arithmétique des surfaces cubique diagonales
    • Diophantine approximation and transcendence theory, Bonn 1985 (ed. G. Wustholz), Springer, Berlin
    • J.-L. COLLIOT-THÉLÈNE, D. KANEVSKY and J.-J. SANSUC, 'Arithmétique des surfaces cubique diagonales', Diophantine approximation and transcendence theory, Bonn 1985 (ed. G. Wustholz), Lecture Notes in Mathematics 1290 (Springer, Berlin, 1987) 1-108.
    • (1987) Lecture Notes in Mathematics , vol.1290 , pp. 1-108
    • Colliot-Thélène, J.-L.1    Kanevsky, D.2    Sansuc, J.-J.3
  • 8
    • 51249195637 scopus 로고
    • On Waring's problem for cubes
    • H. DAVENPORT, 'On Waring's problem for cubes', Acta Math. 71 (1939) 123-143.
    • (1939) Acta Math. , vol.71 , pp. 123-143
    • Davenport, H.1
  • 10
    • 0001409558 scopus 로고
    • Conjectures on elliptic curves over quadratic fields
    • Number theory, Carbondale (ed. M. B. Nathanson), Springer, Berlin
    • D. GOLDFELD, 'Conjectures on elliptic curves over quadratic fields', Number theory, Carbondale (ed. M. B. Nathanson), Lecture Notes in Mathematics 751 (Springer, Berlin, 1979) 108-118.
    • (1979) Lecture Notes in Mathematics , vol.751 , pp. 108-118
    • Goldfeld, D.1
  • 11
    • 0000205228 scopus 로고
    • Heegner points and derivatives of L-series
    • B. H. GROSS and D. ZAGIER, 'Heegner points and derivatives of L-series', Invent. Math. 84 (1986) 225-320.
    • (1986) Invent. Math. , vol.84 , pp. 225-320
    • Gross, B.H.1    Zagier, D.2
  • 12
    • 0009917606 scopus 로고
    • Some problems of "Partitio Numerorum": IV. The singular series in Waring's Problem and the value of the number G(k)
    • G. H. HARDY and J. E. LITTLEWOOD, 'Some problems of "Partitio Numerorum": IV. The singular series in Waring's Problem and the value of the number G(k)', Math. Z. 12 (1922) 161-188.
    • (1922) Math. Z. , vol.12 , pp. 161-188
    • Hardy, G.H.1    Littlewood, J.E.2
  • 13
    • 0010937368 scopus 로고
    • On Waring's problem
    • C. HOOLEY, 'On Waring's problem', Acta Math. 157 (1986) 49-97.
    • (1986) Acta Math. , vol.157 , pp. 49-97
    • Hooley, C.1
  • 14
    • 0042197183 scopus 로고
    • Cubic congruences
    • D. J. LEWIS, 'Cubic congruences', Michigan Math. J. 4 (1957) 85-95.
    • (1957) Michigan Math. J. , vol.4 , pp. 85-95
    • Lewis, D.J.1
  • 15
    • 0009145965 scopus 로고
    • Le groupe de Brauer-Grothendieck en geometrie diophantienne
    • Tome I Gauthier-Villars, Paris
    • Ju. I. MANIN, 'Le groupe de Brauer-Grothendieck en geometrie diophantienne', Actes du Congrès International des Mathématiciens (Nice, 1970), Tome I (Gauthier-Villars, Paris, 1971) 401-411.
    • (1971) Actes du Congrès International des Mathématiciens (Nice, 1970) , pp. 401-411
    • Manin, Ju.I.1
  • 16
    • 0000162218 scopus 로고
    • Un analogue du calcul de Heegner
    • P. SATGÉ, 'Un analogue du calcul de Heegner', Invent. Math. 87 (1987) 425-439.
    • (1987) Invent. Math. , vol.87 , pp. 425-439
    • Satgé, P.1
  • 17
    • 0000579840 scopus 로고
    • Sur certaines hypothèses concernant les nombres premiers
    • A. SCHINZEL and W. SIERPIŃSKI, 'Sur certaines hypothèses concernant les nombres premiers', Acta Arith. 4 (1958) 185-208.
    • (1958) Acta Arith. , vol.4 , pp. 185-208
    • Schinzel, A.1    Sierpiński, W.2
  • 19
    • 85027219806 scopus 로고
    • Ph.D. Thesis, Manchester
    • N. M. STEPHENS, Ph.D. Thesis, Manchester, 1965.
    • (1965)
    • Stephens, N.M.1
  • 20
    • 0001975231 scopus 로고
    • Rational points on certain intersections of two quadrics
    • ed. W. Barth, K. Hulek and H. Lange, Walter de Gruyter, Berlin
    • H. P. F. SWINNERTON-DYER, 'Rational points on certain intersections of two quadrics', Abelian varieties (ed. W. Barth, K. Hulek and H. Lange, Walter de Gruyter, Berlin, 1995) 273-292.
    • (1995) Abelian Varieties , pp. 273-292
    • Swinnerton-Dyer, H.P.F.1
  • 21
    • 84941379277 scopus 로고
    • On Waring's problem for cubes
    • R. C. VAUGHAN, 'On Waring's problem for cubes', J. Reine Angew. Math. 365 (1986) 122-170.
    • (1986) J. Reine Angew. Math. , vol.365 , pp. 122-170
    • Vaughan, R.C.1
  • 22
    • 0000831840 scopus 로고
    • On Waring's problem for cubes II
    • R. C. VAUGHAN, 'On Waring's problem for cubes II', J. London Math. Soc. (2) 39 (1989) 205-218.
    • (1989) J. London Math. Soc. , vol.39 , Issue.2 , pp. 205-218
    • Vaughan, R.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.