Skip to main content
Log in

Reduction of Binary Forms Via the Hyperbolic Centroid

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper we introduce a reduction theory based on the hyperbolic center of mass, which is different from the reduction introduced by Julia (1917). We show that the zero map via the Julia quadratic is different than the hyperbolic center of mass. Moreover, we discover some interesting formulas for computing the hyperbolic centroid.

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

Access this article

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. L. Beshaj, ‘‘Minimal Weierstrass equations for genus 2 curves,’’ arxiv:1612.08318 (2016).

  2. L. Beshaj, ‘‘Reduction theory of binary forms,’’ NATO Sci. Peace Secur., Ser. D: Inf. Commun. Secur. 41, 84–116 (2018).

    MathSciNet  Google Scholar 

  3. L. Beshaj, R. Hidalgo, R. Kruk, A. Malmendier, S. Quispe, and T. Shaska, ‘‘Rational points on the moduli space of genus two,’’ Contemp. Math. 703, 83–115 (2018).

    Article  MathSciNet  Google Scholar 

  4. L. Beshaj and T. Shaska, ‘‘Heights on algebraic curves,’’ NATO Sci. Peace Secur., Ser. D: Inf. Commun. Secur. 41, 137–175 (2018).

    Google Scholar 

  5. J. E. Cremona, ‘‘Reduction of binary cubic and quartic forms,’’ LMS J. Comput. Math. 2, 64–94 (1999).

    Article  MathSciNet  Google Scholar 

  6. G. A. Galperin, ‘‘A concept of the mass center of a system of material points in the constant curvature spaces,’’ Commun. Math. Phys. 154, 63–84 (1993).

    Article  MathSciNet  Google Scholar 

  7. G. Julia, ‘‘Étude sur les formes binaires non quadratiques à indéterminées réelles ou complexes,’’ Mem. Acad. Sci. Inst. Fr. 55, 1–296 (1917).

    Google Scholar 

  8. M. Stoll and J. E. Cremona, ‘‘On the reduction theory of binary forms,’’ J. Reine Angew. Math. 565, 79–99 (2003).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. Elezi or T. Shaska.

Additional information

(Submitted by M. A.Malakhaltsev)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elezi, A., Shaska, T. Reduction of Binary Forms Via the Hyperbolic Centroid. Lobachevskii J Math 42, 84–95 (2021). https://doi.org/10.1134/S199508022101011X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S199508022101011X

Keywords:

Navigation