Theta functions, elliptic functions and π
Heng Huat Chan
Abstract
This book presents several results on elliptic functions and Pi, using Jacobi’s triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan’s work on Pi. The included exercises make it ideal for both classroom use and self-study.
Topics & Concepts
Ramanujan's sumTheta functionEisenstein seriesElliptic functionElliptic integralRamanujan theta functionJacobi elliptic functionsMathematicsIdentity (music)Number theoryAlgebra over a fieldTriple productPure mathematicsIdeal (ethics)Dedekind cutModular formMathematical analysisPhysicsPhilosophyEpistemologyAcousticsAdvanced Mathematical IdentitiesHistory and Theory of MathematicsAnalytic Number Theory Research