Theta Functions Course
Dive into theta functions, exploring their series expansions, convergence, modular transformations, and connections to elliptic functions. Construct explicit models via theta quotients, link them to the Weierstrass ℘-function, and discover their vital roles in elliptic curves, modular forms, and applications in physics, all with rigorous proofs and examples to build deep expertise.

from 4 to 360h flexible workload
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-periodic behaviors. Participants will learn to represent lattices, develop elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and utilize uniqueness and dimension theorems, supported by detailed proofs, practical examples, and tips for accurate, rigorous writing and proper referencing.
Elevify advantages
Develop skills
- Master theta series convergence, including control over domains and holomorphic properties.
- Derive key theta identities such as the heat equation, quasi-periodicity, and modular S-transformation.
- Construct elliptic functions by employing theta quotients to achieve specified divisors.
- Connect theta functions to Weierstrass ℘-function through analysis of poles, zeros, and field extensions.
- Develop skills in writing precise mathematical notes, normalising lattices, monitoring multipliers, 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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