CLASS NUMBERS VIA 3-ISOGENIES AND ELLIPTIC SURFACES-Reference-Cited by-同舟云学术

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CLASS NUMBERS VIA 3-ISOGENIES AND ELLIPTIC SURFACES

Published:2012-11-13 Issue:01 Volume:09 Page:125-137
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

McLEMAN CAM¹,MOODY DUSTIN²

Affiliation:

1. Department of Mathematics, University of Michigan-Flint, Flint, MI 42439, USA

2. National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD, 20899, USA

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 [Formula: see text]. In this sense, this provides a higher-dimensional analog of some recent class number formulas associated to 2-isogenies of elliptic curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304211250128X

Reference7 articles.

1. Bilinear character sums and sum-product problems on elliptic curves

2. Double Character Sums over Elliptic Curves and Finite Fields

3. Character Sums Linked To Elliptic-Curves With Complex Multiplication

4. Certain Exponential Sums and Random Walks on Elliptic Curves

5. Elliptic Curves with Complex Multiplication and a Character Sum

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