Theta Functions Course
This course provides a comprehensive journey through theta functions, starting from series definitions and convergence, progressing to functional equations, transformation laws, and quasi-periodicity. Participants will encode lattices, build elliptic functions with theta quotients, link them to the Weierstrass ℘-function, and apply uniqueness theorems, all supported by detailed proofs, examples, and guidance on precise mathematical writing and referencing.

from 4 to 360h flexible workload
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What will I learn?
Explore theta functions from foundational series convergence and definitions to essential functional equations, transformation properties, and quasi-periodic behaviour. Gain expertise in lattice encoding, elliptic function construction through theta quotients, connections to Weierstrass ℘-function, and applications of uniqueness and dimension theorems, complete with proofs, examples, and tips for rigorous exposition and accurate citations.
Elevify advantages
Develop skills
- Master theta series convergence, domains, and holomorphic properties.
- Derive key theta identities including heat equation and modular laws.
- Construct elliptic functions using theta quotients for given divisors.
- Connect theta functions to Weierstrass ℘ via poles, zeros, and fields.
- Develop skills in rigorous proofs, lattice normalisation, and source citation.
Suggested summary
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