Theta Functions Course
This course guides learners through theta functions, starting from series definitions and convergence, progressing to functional equations, quasi-periodicity, and transformation laws. Participants will construct elliptic functions with theta quotients, link them to the Weierstrass ℘-function, and apply uniqueness theorems, supported by detailed proofs, examples, and tips for precise mathematical writing and referencing sources effectively.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
Explore theta functions comprehensively, covering definitions, convergence, functional equations, transformation laws, and quasi-periodicity. Encode lattices, build elliptic functions through theta quotients, connect to Weierstrass ℘-function, and master uniqueness and dimension results with proofs, examples, and guidance on rigorous exposition and source citation.
Elevify advantages
Develop skills
- Master theta series convergence, domains, and holomorphic properties.
- Derive key theta identities including heat equation and modular laws.
- Construct elliptic functions using theta quotients for divisors.
- Connect theta functions to Weierstrass ℘ via poles, zeros, and fields.
- Develop skills in rigorous proofs, lattice normalisation, and citations.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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