Differential equations satisfied by Eisenstein series of level 2. (English) Zbl 1250.11086
In the paper under review a family of first order differential equations satisfied by certain Eisenstein series of level 2 is derived from the triple and quintuple product identities satisfied by the corresponding Jacobi theta series. Several applications of the differential equations and the product identities are also presented.
Reviewer: Lejla Smajlovic (Sarajevo)
MSC:
| 11M36 | Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) |
| 11F11 | Holomorphic modular forms of integral weight |
| 33E05 | Elliptic functions and integrals |
Keywords:
Eisenstein series; Jacobi theta functions; differential equations; triple product identity; quintuple product identityReferences:
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