Theta Functions Course
Dive into theta functions, progressing from series convergence to modular transformations and elliptic function construction. Learners create theta-quotient representations, connect to Weierstrass ℘-functions, and explore applications in elliptic curves, modular forms, and physics, gaining tools for advanced mathematical research and exposition.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course guides learners from basic theta function definitions and convergence through vital functional equations, transformation properties, and quasi-periodic behaviours. Participants will encode lattices, build elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and leverage uniqueness theorems alongside dimension results, supported by detailed proofs, examples, and tips for accurate writing and 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 achieve 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 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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