ELLIPTIC FUNCTIONS
Academic year and teacher
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- Versione italiana
- Academic year
- 2016/2017
- Teacher
- ANDREA DEL CENTINA
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/03
Training objectives
- To give basic results concerning the elliptic funtions with special regard to the funtion P and P' di Weierstrass and to the addition theorem.
Prerequisites
- Basic concepts and results on function of complex variable: holomorphic functions and their singularities, Cauchy's theorem, Laurent's series, residue theorem.
Course programme
- A brief historical account on elliptic fonctions and the addition theorem, 2 hours; recalls of some properties of the functions of complex variable, 4 hours; periodical meromorphic functions and Jacobi's theorem, 3 hours, simply and double periodical meromorphic funtions, 3 hours; elliptic function, 2 hours; the 4 theorems of Liouville on ellitic functions, 2 hours; the functions P and P' of Weierstrass, 4 hours; Abel's theorem, 2 hours; the field of elliptic functions and the algebraic relation between the P and P' of Weierstrass, 4 hours; addition theorem for the P of Weierstrass, 4 hours; geometric interpretation for the addition theorem, 4 hours; the functions "zeta" and "sigma" of Weierstrass, 4 hours; meromorphic functions satisfying an addition theorem, 6 hours.
Didactic methods
- Lectures in the class room
Learning assessment procedures
- Oral examination, aimed at verifying the complete acquisition of the definitions, and of the main theorems given in the course, including the proofs. The final score will be determined by:
a) comprehension of the definitions and theorens 30%
b) skill in the dedelopment of the proofs 50%
c) language and exposition skills 20%. Reference texts
- Andrea Del Centina, Teoria delle funzioni di una variabile complessa, Aracne, 2010.
