SUMS: Zaman -- The Jacobi Triple Product

This week SSP student Ragib Zaman is giving the talk on the Jacobi Triple product.  

Abstract The Jacobi Triple product formula is a striking identity that equates an
infinite product of some algebraic factors with an infinite sum.  It arises naturally in
the study of Elliptic functions, Lie Algebras and the theory of integer partitions.
Gauss’s circle problem is the problem of counting the number of lattice points contained
within a circle of a given radius, centered at the origin.  After presenting a proof of
the Jacobi Triple Product, we apply it to the generalized problem of counting lattice
points in N dimensional spheres.  If time allows, we will derive a well known special
case of the Jacobi Triple product, Euler’s Pentagonal Number Theorem.