Published: November 06, 2012
Citation: International Journal of Number Theory vol. 9, no. 1, (February 2013) pp. 125-138
Author(s)
C. McLeman, Dustin Moody
Announcement
We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over Fp relates to the class number of the quadratic imaginary number field Q(\sqrt{p}). In this sense, this provides a higher-dimensional analog of some recent class number formulas associated to 2-isogenies of elliptic curves.
We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over Fp relates to the class number of the quadratic imaginary number field Q(\sqrt{p}). In this sense, this provides a higher-dimensional analog of some recent class number...
See full abstract
We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over Fp relates to the class number of the quadratic imaginary number field Q(\sqrt{p}). In this sense, this provides a higher-dimensional analog of some recent class number formulas associated to 2-isogenies of elliptic curves.
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Keywords
elliptic curve; elliptic surface; class number; character sum
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