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1996-1997 | 78 | 2 | 101-123
Tytuł artykułu

Euler's concordant forms

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
78
Numer
2
Strony
101-123
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-10-16
poprawiono
1996-03-11
Twórcy
autor
  • School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
  • Department of Mathematics, Penn State University, University Park, Pennsylvania 16802, U.S.A.
Bibliografia
  • [1] E. T. Bell, The problems of congruent numbers and concordant forms, Proc. Amer. Acad. Sci. 33 (1947), 326-328.
  • [2] M. Bennett, private communication.
  • [3] D. Bump, S. Friedberg and J. Hoffstein, Nonvanishing theorems for L-functions of modular forms and their derivatives, Invent. Math. 102 (1990), 543-618.
  • [4] J. Coates and A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), 223-251.
  • [5] F. Diamond and K. Kramer, Modularity of a family of elliptic curves, Math. Res. Lett. 2 (3) (1995), 299-304.
  • [6] L. Euler, De binis formulis speciei xx+myy et xx+nyy inter se concordibus et disconcordibus, Opera Omnia Series 1 vol. 5 (1780), 48-60, Leipzig-Berlin-Zürich, 1944.
  • [7] D. Husemöller, Elliptic Curves, Springer, New York, 1987.
  • [8] A. Knapp, Elliptic Curves, Princeton Univ. Press, 1992.
  • [9] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, 1984.
  • [10] V. A. Kolyvagin, Finiteness of E(ℚ) and the Tate-Shafarevich group of E(ℚ) for a subclass of Weil curves, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 522-540 (in Russian).
  • [11] J. Lehman, Levels of positive definite ternary quadratic forms, Math. Comp. 58, 197 (1992), 399-417.
  • [12] L. Mai and M. R. Murty, A note on quadratric twists of an elliptic curve, in: Elliptic Curves and Related Topics, CRM Proc. Lecture Notes, Amer. Math. Soc., 1994, 121-124.
  • [13] D. Masser and J. Rickert, Simultaneous Pell equations, J. Number Theory, to appear.
  • [14] M. R. Murty and V. K. Murty, Mean values of derivatives of modular L-series, Ann. of Math. 133 (1991), 447-475.
  • [15] K. Ono, Rank zero quadratic twists of modular elliptic curves, Compositio Math., to appear.
  • [16] K. Ono, Twists of elliptic curves, Compositio Math., to appear.
  • [17] T. Ono, Variations on a Theme of Euler, Plenum, New York, 1994.
  • [18] J. Rickert, Simultaneous rational approximations and related Diophantine equations, Math. Proc. Cambridge Philos. Soc. 113 (1993), 461-472.
  • [19] H. P. Schlickewei, The number of subspaces occurring in the p-adic subspace theorem in Diophantine approximation, J. Reine Angew. Math. 406 (1990), 44-108.
  • [20] W. M. Schmidt, Norm form equations, Ann. of Math. 96 (1972), 526-551.
  • [21] W. M. Schmidt, Diophantine Approximations, Lecture Notes in Math. 785, Springer, 1980.
  • [22] B. Schoeneberg, Das Verhalten von mehrfachen Thetareihen bei Modulsubstitutionen, Math. Ann. 116 (1939), 511-523.
  • [23] J.-P. Serre, Divisibilité de certaines fonctions arithmétiques, Enseign. Math. 22 (1976), 227-260.
  • [24] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971.
  • [25] G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481.
  • [26] C. Siegel, Über die analytische Theorie der quadratischen formen, in: Gesammelte Abhandlungen, Bd. 3, Springer, 1966, 326-405.
  • [27] J. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
  • [28] J. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, New York, 1992.
  • [29] J. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math. 72 (1983), 323-334.
  • [30] J. L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484.
  • [31] A. Wiles, Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. 141 (1995), 443-551.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav78i2p101bwm
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