Gaussian hypergeometric evaluations of traces of Frobenius for elliptic curves
Author:
Catherine Lennon
Journal:
Proc. Amer. Math. Soc. 139 (2011), 19311938
MSC (2010):
Primary 11T24, 11G20
Published electronically:
November 3, 2010
MathSciNet review:
2775369
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Abstract: We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve over satisfying and in terms of special values of Gaussian hypergeometric series. This paper uses methods introduced by Fuselier for oneparameter families of curves to express the trace of Frobenius of as a function of its invariant and discriminant instead of a parameter, which are more intrinsic characteristics of the curve.
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Additional Information
Catherine Lennon
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email:
clennon@math.mit.edu
DOI:
http://dx.doi.org/10.1090/S000299392010106093
PII:
S 00029939(2010)106093
Received by editor(s):
March 22, 2010
Received by editor(s) in revised form:
May 28, 2010
Published electronically:
November 3, 2010
Additional Notes:
This work was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Communicated by:
Matthew A. Papanikolas
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
