Skip to main content
SpringerLink
Log in

Some exact formulae for the numbers of representations of integers by ternary quadratic forms

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper we shall give some exact formulae for the numbers of representations of integers by certain ternary quadratic forms whose genus have class numbers large 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.A. Antoniadi S,M. Bungert and G. Frey, Properties of twists of elliptic curves, J.reine angew.Math. 405(1990), 1–28.

    MathSciNet  Google Scholar 

  2. J.E. Cremona, Algorithms for modular elliptic curves, Cambridge Univ. Press 1992.

  3. Y. Choie, Y. Chung and X.L.Wang, The values of theta function at cusp points and the number of representation in the genus of quadratic forms, preprint(2002).

  4. W. Duke and R. Schulze-Pillot, Representations of integers by positive definite ternary quadratic forms and equidistribution of lattice points on ellipsoids. Invent. Math. 99 (1990), 49–57.

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Jones, The arithmetic theory of quadratic forms, Mathematical Association of America, 1950.

  6. I. Kaplansky, The first nontrivial genus of positive definite ternary forms, Math. Comp. 64 (1995), 341–345.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Y. Pei, Eisenstein series of weight 3/2: I, II, Trans. Amer. Math. Soc. 274 (1982), 573–606 and 283 (1984), 589-603.

    MathSciNet  MATH  Google Scholar 

  8. D. Y.Pei, G.Rosenberger and Xueli Wang, The eligible numbers of positive definite ternary forms, to appear in Math.Zeit.(2000).

  9. G. Shimura, On modular forms of half integral weight, Ann. of Math. 97 (1973), 440–481.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Schulze-Pillot, Thetareihen positiver definiter quadratischer Formen, Invent. Math. 75 (1984), 283–299.

    Article  MathSciNet  MATH  Google Scholar 

  11. J.B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent.Math. 72, (1983), 323–334.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Zhao, A criterion for elliptic curves with lowest 2-power in L(1), Math.Proc.Camb.Phil.Soc.,121,(1997), 385–400.

    Article  MATH  Google Scholar 

  13. C. Zhao, A criterion for elliptic curves with second lowest 2-power in L(1), to appear.

  14. C. Zhao, A criterion for elliptic curves with second lowest 2-power in L(l)(II),in press.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hunan University, Changsha, 410082, P. R. China

    Xueli Wang

  2. Department of Mathematics, Guangzhou University, Guangzhou, 510405, P. R. China

    Xueli Wang

  3. State key Lab. of Information Security, Beijing, 100039

    Xueli Wang

  4. Department of Mathematics, Peking University, Beijing, 100871, P. R. China

    Chunlai Zhao

Authors
  1. Xueli Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunlai Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xueli Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, X., Zhao, C. Some exact formulae for the numbers of representations of integers by ternary quadratic forms. Results. Math. 45, 370–388 (2004). https://doi.org/10.1007/BF03323390

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323390

Keywords

Search

Navigation