An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

IIT Madras Course , Prof. T.E. Venkata Balaji

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Lecture 31: The Uniqueness Property of the Weierstrass Phe-function

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        An Introduction to Riemann Surfaces and Algebraic Curves Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit httpwww.nptel.iitm.ac.insyllabus111106044Goals To show that the Weierstrass Phe-function is the unique doubly-periodic meromorphic function (i.e., the unique elliptic function) with residue-zero double poles precisely at each point of the lattice and with constant term zero in the Laurent development at the originKeywords Upper half-plane, lattice (or) grid in the plane, fundamental parallelogram (or) period parallelogram associated to a lattice, complex torus associated to a lattice, doubly-periodic meromorphic function (or) elliptic function associated to a lattice, Weierstrass phe-function associated to a lattice, isolated double pole, singular part of the Laurent expansion, deleted neighborhood, even function, entire function, algebraic elliptic cubic curve

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