The joy of multisection: elementary approaches to Ramanujan’s lacunary identities for Bernoulli numbers

Key Points

• Ramanujan’s lacunary identities reveal new relationships within the framework of Bernoulli numbers.
• The geometric approach emphasizes how symmetries within the complex plane affect summation domains significantly.
• Assessment using generating functions extends these identities to connections with Eisenstein’s series, enriching the mathematical landscape.
• These findings may facilitate deeper insights into the structural properties of special functions in number theory.

Abstract