Transactions of the American Mathematical Society · 1994 · 43 citations · 1 references
Natural SciencesMathematicsPhysicsAlgebraNumber TheoryTheoretical PhysicsAlgebraic Number TheoryArithmetic GeometryElliptic CurvesGenerating FunctionsModular ArithmeticModular FormsElliptic FunctionsElliptic Modular FormsExplicit FormulaeModular Form ComputationsModular PolynomialsRamanujan SumTheta FunctionsTheta Series
We examine the connection between the additive formulae of the theta functions, the Fourier series expansion of the 12 elliptic functions, and the logarithmic derivatives of the theta functions. As an application, we study the Lambert series related to the modular equations of degree 5 and many interesting identities of Ramanujan are found in this process.
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