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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 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 utilise 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 S-transformation.
  • Construct elliptic functions via theta quotients to achieve specific divisors.
  • Link theta functions to Weierstrass ℘ by analysing poles, zeros, and field extensions.
  • Produce precise mathematical notes with lattice normalisation, multiplier tracking, and proper citations.

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
Workload: between 4 and 360 hours

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