Theta Functions Course
Dive into theta functions, starting with series convergence and progressing to modular transformations and elliptic functions. Construct theta-quotient representations, connect to Weierstrass ℘-functions, and discover their applications in elliptic curves, modular forms, and physics, with rigorous proofs and practical examples to build deep understanding.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
This course guides you from basic theta function definitions and convergence through vital functional equations, transformation rules, and quasi-periodic properties. You will learn to represent lattices, build elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and use uniqueness and dimension theorems, supported by detailed proofs, examples, and tips for clear, precise writing with proper references.
Elevify advantages
Develop skills
- Master theta series convergence, including control over domains and holomorphic properties.
- Derive essential theta identities like the heat equation, quasi-periodicity, and modular S-transformation.
- Construct elliptic functions by applying theta quotients to specified divisors.
- Link theta functions to Weierstrass ℘-function via poles, zeros, and field structures.
- Develop skills in writing precise mathematical notes, normalising lattices, and citing sources accurately.
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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