Elliptic Functions and the Ramanujan Octave

Equality

The complete elliptic integral of the first kind provides the k modulus which is shown to connect these integrals and functions to the modular functions previously used for calculating the class invariant and the octic q continued fraction.  The k modulus is an algebraic integer between 0 and 1.  Equations are developed for odd and even class invariants and their associated octahedron.  The connection to the Elliptic Theta functions and the j-invariant is also shown.

Elliptic Functions and the Ramanujan Octave

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s