This paper discusses several properties of the Weierstrass-℘ function, as defined on the fundamental parallelogram C/Γ, where C is the complex plane and Γ is the lattice generated by ω1 and ω2. Using the addition formula for ℘(z1 + z2), we develop a reccurence relation for ℘(nz) in terms of ℘(z). We then examine the degree of this expression, some coefficients, and patterns concerning the poles of this function. We also consider the geometric interpretation of taking an arbitrary z0 and adding it to itself, both in the fundamental parallelogram C/Γ and the elliptic curve generated by ℘(z) and ℘′(z).
Faculty Advisor Name
Faculty Advisor Institution
Texas A&M University
Suggested Mathematics Subject Classification(s)
Primary 54C40, 14E20; Secondary 46E25, 20C20
Walter H. Chen and Michael S. Willis, Properties of the Iterates of the Weierstrass-℘ Function, Furman University Electronic Journal of Undergraduate Mathematics, 9 (2016), 36-43. Available at: http://scholarexchange.furman.edu/fuejum/vol9/iss1/3