Theta Functions Course
Dive deep into theta functions, covering their series expansions, convergence, modular transformations, and connections to elliptic functions. Construct practical theta-quotient representations, explore links with the Weierstrass ℘-function, and discover applications in elliptic curves, modular forms, and theoretical physics, with rigorous proofs and examples for solid understanding.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This course provides a structured journey through theta functions, starting from fundamental definitions and convergence properties, progressing to essential functional equations, transformation laws, and quasi-periodicity. Participants will learn to represent lattices using theta functions, develop elliptic functions through theta quotients, connect them to the Weierstrass ℘-function, and utilise uniqueness and dimension theorems, supported by detailed proofs, examples, and tips for accurate mathematical writing and referencing.
Elevify advantages
Develop skills
- Master theta series convergence, including control over domains and holomorphic properties.
- Derive key theta identities such as heat equation solutions, quasi-periodicity, and modular transformations.
- Construct elliptic functions using theta quotients to achieve specific divisors.
- Connect theta functions to Weierstrass ℘-function by analysing poles, zeros, and field extensions.
- Develop skills in writing precise mathematical notes, normalising lattices, and proper source citation.
Suggested summary
Before starting, you can change the chapters and the 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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