Theta Functions Course
Dive into theta functions, starting from their series expansions and convergence up to modular transformations and connections with elliptic functions. Construct practical theta-quotient representations, explore ties to the Weierstrass ℘-function, and discover their vital roles in elliptic curves, modular forms, and physics applications, all with solid proofs and examples.

from 4 to 360h flexible workload
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 encode lattices, build elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and use uniqueness and dimension theorems, complete with proofs, examples, and tips for clear, rigorous writing and proper referencing.
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 extensions.
- Develop skills in writing precise mathematical notes, normalising lattices, and citing references 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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