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.
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REFERENCES
L. Beshaj, ‘‘Minimal Weierstrass equations for genus 2 curves,’’ arxiv:1612.08318 (2016).
L. Beshaj, ‘‘Reduction theory of binary forms,’’ NATO Sci. Peace Secur., Ser. D: Inf. Commun. Secur. 41, 84–116 (2018).
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).
L. Beshaj and T. Shaska, ‘‘Heights on algebraic curves,’’ NATO Sci. Peace Secur., Ser. D: Inf. Commun. Secur. 41, 137–175 (2018).
J. E. Cremona, ‘‘Reduction of binary cubic and quartic forms,’’ LMS J. Comput. Math. 2, 64–94 (1999).
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).
G. Julia, ‘‘Étude sur les formes binaires non quadratiques à indéterminées réelles ou complexes,’’ Mem. Acad. Sci. Inst. Fr. 55, 1–296 (1917).
M. Stoll and J. E. Cremona, ‘‘On the reduction theory of binary forms,’’ J. Reine Angew. Math. 565, 79–99 (2003).
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(Submitted by M. A.Malakhaltsev)
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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
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DOI: https://doi.org/10.1134/S199508022101011X