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Full-Text Articles in Number Theory
The Conditional Probability That An Elliptic Curve Has A Rational Subgroup Of Order 5 Or 7, Meagan Kenney
The Conditional Probability That An Elliptic Curve Has A Rational Subgroup Of Order 5 Or 7, Meagan Kenney
Senior Projects Spring 2019
Let E be an elliptic curve over the rationals. There are two different ways in which the set of rational points on E can be said to be divisible by a prime p. We will call one of these types of divisibility local and the other global. Global divisibility will imply local divisibility; however, the converse is not guaranteed. In this project we focus on the cases where p=5 and p=7 to determine the probability that E has global divisibility by p, given that E has local divisibility by p.
Factorization Lengths In Numerical Monoids, Maya Samantha Schwartz
Factorization Lengths In Numerical Monoids, Maya Samantha Schwartz
Senior Projects Spring 2019
A numerical monoid M generated by the natural numbers n_1, ..., n_k is a subset of {0, 1, 2, ...} whose elements are non-negative linear combinations of the generators n_1, ..., n_k. The set of factorizations of an element in M is the set of all the different ways to write that element as a linear combination of the generators. The length of a factorization of an element is the sum of the coefficients of that factorization. Since an element in a monoid can be written in different ways in terms of the generators, its set of factorization lengths may …