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Theta Functions Course

Theta Functions Course
from 4 to 360h flexible workload
valid certificate in your country

What will I learn?

This course guides learners from fundamental theta function definitions and convergence through essential 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 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 essential theta identities such as the heat equation, quasi-periodicity, and modular S-transformation.
  • Construct elliptic functions by employing theta quotients to achieve specified divisors.
  • Establish links between theta functions and Weierstrass ℘-function via poles, zeros, and field extensions.
  • Produce precise mathematical notes by standardising lattices, monitoring multipliers, and properly citing references.

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.
Workload: between 4 and 360 hours

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