Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Levels of positive definite ternary quadratic forms


Author: J. Larry Lehman
Journal: Math. Comp. 58 (1992), 399-417, S17
MSC: Primary 11E20
MathSciNet review: 1106974
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The level N and squarefree character q of a positive definite ternary quadratic form are defined so that its associated modular form has level N and character $ {\chi _q}$. We define à collection of correspondences between classes of quadratic forms having the same level and different discriminants. This makes practical a method for finding representatives of all classes of ternary forms having a given level. We also give a formula for the number of genera of ternary forms with a given level and character.


References [Enhancements On Off] (What's this?)

  • [1] Heinrich Brandt and Oskar Intrau, Tabellen reduzierter positiver ternärer quadratischer Formen, Abh. Sächs. Akad. Wiss. Math.-Nat. Kl. 45 (1958), no. 4, 261 (German). MR 0106204
  • [2] H. Cohen and J. Oesterlé, Dimensions des espaces de formes modulaires, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Springer, Berlin, 1977, pp. 69–78. Lecture Notes in Math., Vol. 627 (French). MR 0472703
  • [3] J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1988. With contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 920369
  • [4] L. E. Dickson, Studies in the theory of numbers, The University of Chicago Press, Chicago, 1930.
  • [5] Hiroaki Hijikata, Arnold K. Pizer, and Thomas R. Shemanske, The basis problem for modular forms on Γ₀(𝑁), Mem. Amer. Math. Soc. 82 (1989), no. 418, vi+159. MR 960090, 10.1090/memo/0418
  • [6] Burton W. Jones, The Arithmetic Theory of Quadratic Forms, Carcus Monograph Series, no. 10, The Mathematical Association of America, Buffalo, N. Y., 1950. MR 0037321
  • [7] Neal Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, vol. 97, Springer-Verlag, New York, 1984. MR 766911
  • [8] J. Larry Lehman, Rational points on elliptic curves with complex multiplication by the ring of integers in 𝑄(√-7), J. Number Theory 27 (1987), no. 3, 253–272. MR 915499, 10.1016/0022-314X(87)90066-7
  • [9] Bruno Schoeneberg, Elliptic modular functions: an introduction, Springer-Verlag, New York-Heidelberg, 1974. Translated from the German by J. R. Smart and E. A. Schwandt; Die Grundlehren der mathematischen Wissenschaften, Band 203. MR 0412107
  • [10] R. Schulze-Pillot, Thetareihen positiv definiter quadratischer Formen, Invent. Math. 75 (1984), no. 2, 283–299 (German). MR 732548, 10.1007/BF01388566
  • [11] J.-P. Serre and H. M. Stark, Modular forms of weight 1/2, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Springer, Berlin, 1977, pp. 27–67. Lecture Notes in Math., Vol. 627. MR 0472707
  • [12] Goro Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481. MR 0332663

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11E20

Retrieve articles in all journals with MSC: 11E20


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1106974-1
Article copyright: © Copyright 1992 American Mathematical Society