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A new identity for the tenth power of the Dedekind eta‐funtion η( z ) is established. This is used to give a short proof of Ramanujan's congruence  p (11 n +6) ≡0 (mod 11) and to prove the lacunarity of η 10 ( z ). Various related identities, many connected to Eisenstein series and some from Ramanujan's lost notebook, are established.

A New Identity for ( q ; q ) ∞ 10 with an Application to Ramanujan's Partition Congruence Modulo 11