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Addition formulas for Jacobi’s theta functions, Dedekind’s eta function, and Ramanujan’s congruences. (English) Zbl 1169.33005
The author proves some new theta function identities, as well as series expansions for particular powers of Dedekind’s eta function. As corollaries, known Ramanujan-type congruences for the partition function are derived.

MSC:
33E05 Elliptic functions and integrals
11F11 Holomorphic modular forms of integral weight
11F20 Dedekind eta function, Dedekind sums
11F27 Theta series; Weil representation; theta correspondences
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