Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity
نویسندگان
چکیده
منابع مشابه
Partition Identities Arising from Theta Function Identities
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In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially specializations of a so-called universal mock theta function g3(z, q) of Gordon–McIntosh. Here we show that g3 arises naturally from the reciprocal of the classical Jacobi triple product—and is intimately ...
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Ramanujan’s partition congruences can be proved by first showing that the coefficients in the expansions of (q; q)∞ satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r , the coefficients in the expansions of (q; q)∞ satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to ...
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We describe a new series of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan. Introduction Let z ∈ H = {x+ yi : x, y ∈ R, y > 0} and for each x ∈ R set q = exp(2πixz) and e(x) = exp(2πix). The Dede...
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ژورنال
عنوان ژورنال: European Journal of Pure and Applied Mathematics
سال: 2018
ISSN: 1307-5543
DOI: 10.29020/nybg.ejpam.v11i1.3222