Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Some theorems and conjectures in diophantine equations
HTML articles powered by AMS MathViewer

by Serge Lang PDF
Bull. Amer. Math. Soc. 66 (1960), 240-249
References
  • B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102–105. MR 97359, DOI 10.1112/S0025579300001145
  • J. W. S. Cassels, Arithmetic on curves of genus $1$. I. On a conjecture of Selmer, J. Reine Angew. Math. 202 (1959), 52–99. MR 109136, DOI 10.1515/crll.1959.202.52
  • François Châtelet, Méthode galoisienne et courbes de genre un, Ann. Univ. Lyon Sect. A (3) 9 (1946), 40–49 (French). MR 20575
  • François Châtelet, Variations sur un thème de H. Poincaré, Ann. Sci. École Norm. Sup. (3) 61 (1944), 249–300 (French). MR 0014720, DOI 10.24033/asens.918
  • 5. C. Chevalley, Démonstration d’une hypothèse de M. Artin, Abh. Math. Sem. Univ. Hamburg vol. 11 (1935) pp. 73-75.
  • Serge Lang, On quasi algebraic closure, Ann. of Math. (2) 55 (1952), 373–390. MR 46388, DOI 10.2307/1969785
  • Serge Lang, The theory of real places, Ann. of Math. (2) 57 (1953), 378–391. MR 53924, DOI 10.2307/1969865
  • 8. S. Lang, Algebraic groups over finite fields, Amer. J. Math. vol. 78 no. 3 (1956) pp. 555—563.
  • Serge Lang, Integral points on curves, Inst. Hautes Études Sci. Publ. Math. 6 (1960), 27–43. MR 130219, DOI 10.1007/BF02698777
  • S. Lang and A. Néron, Rational points of abelian varieties over function fields, Amer. J. Math. 81 (1959), 95–118. MR 102520, DOI 10.2307/2372851
  • Serge Lang and John Tate, Principal homogeneous spaces over abelian varieties, Amer. J. Math. 80 (1958), 659–684. MR 106226, DOI 10.2307/2372778
  • D. J. Lewis, Cubic homogeneous polynomials over $p$-adic number fields, Ann. of Math. (2) 56 (1952), 473–478. MR 49947, DOI 10.2307/1969655
  • 13. K. Mahler, Über die rationalen Punkte auf Kurven vom Geschlecht Eins, J. Reine Angew. Math. vol. 170 (1934) pp. 168-178. 14. L. J. Mordell, On the rational solutions of the indeterminate equation of the third and fourth degrees, Proc. Cambridge Philos. Soc. vol. 21 (1922) pp. 179-192.
  • Tadasi Nakayama, Cohomology of class field theory and tensor product modules. I, Ann. of Math. (2) 65 (1957), 255–267. MR 90620, DOI 10.2307/1969962
  • André Néron, Problèmes arithmétiques et géométriques rattachés à la notion de rang d’une courbe algébrique dans un corps, Bull. Soc. Math. France 80 (1952), 101–166 (French). MR 56951, DOI 10.24033/bsmf.1427
  • L. G. Peck, Diophantine equations in algebraic number fields, Amer. J. Math. 71 (1949), 387–402. MR 28896, DOI 10.2307/2372253
  • Ernst S. Selmer, The Diophantine equation $ax^3+by^3+cz^3=0$, Acta Math. 85 (1951), 203–362 (1 plate). MR 41871, DOI 10.1007/BF02395746
  • I. R. Shafarevich, Birational equivalence of elliptical curves, Dokl. Akad. Nauk SSSR (N.S.) 114 (1957), 267–270 (Russian). MR 0094349
  • 20. C. L. Siegel, Über einige Anwendungen Diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys. Math. Kl. (1929) pp. 41-69.
  • John Tate, Galois cohomology, Arithmetic algebraic geometry (Park City, UT, 1999) IAS/Park City Math. Ser., vol. 9, Amer. Math. Soc., Providence, RI, 2001, pp. 465–479. MR 1857470, DOI 10.1090/pcms/009/07
  • André Weil, On algebraic groups and homogeneous spaces, Amer. J. Math. 77 (1955), 493–512. MR 74084, DOI 10.2307/2372637
  • 23. A. Weil, L’arithmétique sur les courbes algébriques, Acta Math. vol. 52 (1928) pp. 281-315.
  • André Weil, The field of definition of a variety, Amer. J. Math. 78 (1956), 509–524. MR 82726, DOI 10.2307/2372670
  • André Weil, Variétés abéliennes et courbes algébriques, Publ. Inst. Math. Univ. Strasbourg, vol. 8, Hermann & Cie, Paris, 1948 (French). MR 0029522
  • 26. E. Witt, Theorie der quadratischen Formen in beliebigen Körper, J. Reine Angrew. Math. vol. 176 (1937) pp. 31-44. 27. E. Witt, Zerlegung reeller algebraische Funktionen in Quadrate, J. Reine Angew. Math. vol. 171 (1934) pp. 4-11.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 66 (1960), 240-249
  • DOI: https://doi.org/10.1090/S0002-9904-1960-10440-5
  • MathSciNet review: 0118698