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

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'll encode lattices, build elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and use uniqueness theorems, all with solid proofs, examples, and tips for clear 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 transformations.
- Construct elliptic functions via theta quotients to match specific divisors.
- Link theta functions to Weierstrass ℘ by analysing poles, zeros, and field extensions.
- Develop skills in rigorous mathematical writing, lattice normalisation, multiplier tracking, and source citation.
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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