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Showing 1 to 2 of 2 for “"cubic theta-functions"”.
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Cubic theta functions and identities for Appell's F1 function
… centered around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a class of two-variable cubic modular equations. Chapter 2 is dedicated to the rst two topics, while Chapter 3 covers the last. First, the theory of cubic …
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Modular equations and Ramanujan's cubic and quartic theories of theta functions
… several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered by Somos and establish applications of some of them. In Chapter 3, we will give proofs for several Dedekind eta product identities which Somos …