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
DOI: https://doi.org/10.1090/S0025-5718-1992-1106974-1
MathSciNet review: 1106974
Full-text PDF

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] H. Brandt and O. Intrau, Tabellen reduzierter positiver ternärer quadratischer Formen, Abh. Sächs. Akad. Wiss. Leipzig Math.-Natur. Kl. 45 (1958). MR 0106204 (21:4938)
  • [2] H. Cohen and J. Oesterlé, Dimensions des espaces deformes modulaires, Lecture Notes in Math., vol. 627, Springer-Verlag, Berlin, 1977. MR 0472703 (57:12396)
  • [3] J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Springer-Verlag, New York, 1988. MR 920369 (89a:11067)
  • [4] L. E. Dickson, Studies in the theory of numbers, The University of Chicago Press, Chicago, 1930.
  • [5] H. Hijikata, A. Pizer, and T. Shemanske, The basis problem for modular forms on $ {\Gamma _0}(N)$, Mem. Amer. Math. Soc. No. 82 (1989), 1-159. MR 960090 (90d:11056)
  • [6] B. W. Jones, The arithmetic theory of quadratic forms, Math. Assoc. America and Wiley, New York, 1950. MR 0037321 (12:244a)
  • [7] N. Koblitz, Introduction to elliptic curves and modular forms, Springer-Verlag, New York, 1984. MR 766911 (86c:11040)
  • [8] J. L. Lehman, Rational points on elliptic curves with complex multiplication by the ring of integers in $ \mathbb{Q}(\sqrt { - 7} )$, J. Number Theory 27 (1987), 253-272. MR 915499 (89a:11059)
  • [9] B. Schoeneberg, Elliptic modular functions, an introduction, Springer-Verlag, New York, 1974. MR 0412107 (54:236)
  • [10] R. Schulze-Pillot, Thetareihen positiv definiter quadratischer Formen, Invent. Math. 75 (1984), 283-299. MR 732548 (86d:11042)
  • [11] J.-P. Serre and H. M. Stark, Modular forms of weight $ \frac{1}{2}$, Lecture Notes in Math., vol. 627, Springer-Verlag, Berlin, 1977. MR 0472707 (57:12400)
  • [12] G. Shimura, On modular forms of half-integral weight, Ann. of Math. (2) 97 (1973), 440-481. MR 0332663 (48:10989)

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

American Mathematical Society