Lethbridge Number Theory and Combinatorics Seminar: Manoj Kumar
Topic
The Signs in an Elliptic Net
Speakers
Details
Let $R$ be an integral domain and let $A$ be a finitely generated free abelian group.
An elliptic net is a map $W \colon A\longrightarrow R$ with $W(0)=0$, and such that for all $p,q,r,s \in A$, \begin{multline*}
W(p+q+s) \, W(p-q) \, W(r+s) \, W(r)\\
+W(q+r+s) \, W(q-r) \, W(p+s) \, W(p)\\
+W(r+p+s) \, W(r-p) \, W(q+s) \, W(q)=0.
\end{multline*}
In this talk we will give a formula to compute the sign of any term of an elliptic net without actually computing the value of that term.
An elliptic net is a map $W \colon A\longrightarrow R$ with $W(0)=0$, and such that for all $p,q,r,s \in A$, \begin{multline*}
W(p+q+s) \, W(p-q) \, W(r+s) \, W(r)\\
+W(q+r+s) \, W(q-r) \, W(p+s) \, W(p)\\
+W(r+p+s) \, W(r-p) \, W(q+s) \, W(q)=0.
\end{multline*}
In this talk we will give a formula to compute the sign of any term of an elliptic net without actually computing the value of that term.