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Elliptic curves

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Full-Text Articles in Number Theory

A Variation On The Theme Of Nicomachus, Florian Luca, Geremías Polanco, Wadim Zudilin Mar 2018

A Variation On The Theme Of Nicomachus, Florian Luca, Geremías Polanco, Wadim Zudilin

Mathematics Sciences: Faculty Publications

In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square.

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Computing Local Constants For Cm Elliptic Curves, Sunil Chetty, Lung Li Jan 2014

Computing Local Constants For Cm Elliptic Curves, Sunil Chetty, Lung Li

Mathematics Faculty Publications

Let E/k be an elliptic curve with CM by O. We determine a formula for (a generalization of) the arithmetic local constant of Mazur-Rubin at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to describe extensions F/Q over which the O-rank of E grows.

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Elliptic Curves Of High Rank, Cecylia Bocovich Apr 2012

Elliptic Curves Of High Rank, Cecylia Bocovich

Mathematics, Statistics, and Computer Science Honors Projects

The study of elliptic curves grows out of the study of elliptic functions which dates back to work done by mathematicians such as Weierstrass, Abel, and Jacobi. Elliptic curves continue to play a prominent role in mathematics today. An elliptic curve E is defined by the equation, y2 = x3 + ax + b, where a and b are coefficients that satisfy the property 4a3 + 27b2 = 0. The rational solutions of this curve form a group. This group, denoted E(Q), is known as the Mordell-Weil group and was proved by Mordell to be isomorphic …

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Galois Structure And De Rhan Invariants Of Elliptic Curves, Darren B. Glass, Sonin Kwon Jan 2009

Galois Structure And De Rhan Invariants Of Elliptic Curves, Darren B. Glass, Sonin Kwon

Math Faculty Publications

Let K be a number field with ring of integers OK. Suppose a finite group G acts numerically tamely on a regular scheme X over OK. One can then define a de Rham invariant class in the class group Cl(OK[G]), which is a refined Euler characteristic of the de Rham complex of X. Our results concern the classification of numerically tame actions and the de Rham invariant classes. We first describe how all Galois etale G-covers of a K-variety may be built up from finite Galois extensions of K and from geometric covers. When X is a curve of positive …

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