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Class invariants from a new kind of Weber-like modular equation
Get PDFA technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method. They are obtained by means of specialising certain modular equations related to Weber's modular equations of `irrational type'. The technique works for certain eta quotients evaluated at points in an imaginary quadratic field with discriminant d1 (mod 8)
Generalized mth order Jacobi theta functions and the Macdonald identities
Get PDF10.1142/S1793042108001456International Journal of Number Theory43461-47
Representations of certain binary quadratic forms as Lambert series
No full text10.4064/aa143-3-3Acta Arithmetica1433227-23
Differential equations satisfied by Eisenstein series of level 2
No full textRamanujan’s differential equations for the classical Eisenstein series are of great importance to many areas in number theory and special functions. H.H. Chan recently demonstrated that these differential equations can be derived from the triple product identity and the quintuple product identity in an elementary manner. In this article, we extend this method in a uniform manner to derive corresponding differential equations for the Eisenstein series of level 2. Several applications of these differential equations are also given.Accepted versio
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