## Lethbridge Number Theory and Combinatorics Seminar: Jeff Bleaney

- Date: 10/07/2013
- Time: 12:00

Lecturer(s):
Jeff Bleaney,

*University of Lethbridge*
Location:

University of Lethbridge

Topic:

Symmetries of an Elliptic Net

Description:

In 1948, Morgan Ward introduced the concept of an Elliptic Divisibility Sequence (EDS) as an integer sequence $(W_{n})$ which satisfies the recurrence relation $$W_{m+n}W_{m-n}W_{1}^{2} = W_{m+1}W_{m-1}W_{n}^{2} - W_{n+1}W_{n-1}W_{m}^{2},$$ and satisfies the additional property that $W_{m}|W_{n}$ whenever $m|n$. Of particular interest to Ward, were what he called symmetries of an EDS. Ward showed that if $(W_{n})$ is an EDS with $W_{r} = 0$, then we have $$W_{r+i} = ab^{i}W_{i},$$ for some $a$ and $b$.

In her Ph.\,D.\ thesis in 2008, Kate Stange generalized the concept of an EDS to an $n$-dimensional array called an Elliptic Net.

\par

We will discuss the connections between EDS's, Elliptic Nets, and elliptic curves, and give a generalization of Ward's symmetry theorem for elliptic nets.

In 1948, Morgan Ward introduced the concept of an Elliptic Divisibility Sequence (EDS) as an integer sequence $(W_{n})$ which satisfies the recurrence relation $$W_{m+n}W_{m-n}W_{1}^{2} = W_{m+1}W_{m-1}W_{n}^{2} - W_{n+1}W_{n-1}W_{m}^{2},$$ and satisfies the additional property that $W_{m}|W_{n}$ whenever $m|n$. Of particular interest to Ward, were what he called symmetries of an EDS. Ward showed that if $(W_{n})$ is an EDS with $W_{r} = 0$, then we have $$W_{r+i} = ab^{i}W_{i},$$ for some $a$ and $b$.

In her Ph.\,D.\ thesis in 2008, Kate Stange generalized the concept of an EDS to an $n$-dimensional array called an Elliptic Net.

\par

We will discuss the connections between EDS's, Elliptic Nets, and elliptic curves, and give a generalization of Ward's symmetry theorem for elliptic nets.

Other Information:

Location: B660 University HallWeb page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/