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• W2949062918 abstract "Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms. The analytic theory of partial theta functions however, which have $q$-expansions resembling modular theta functions, is not well understood. Here we consider families of $q$-hypergeometric series which converge in two disjoint domains. In one domain, we show that these series are often equal to one another, and define mock theta functions, including the classical mock theta functions of Ramanujan, as well as certain combinatorial generating functions, as special cases. In the other domain, we prove that these series are typically not equal to one another, but instead are related by partial theta functions." @default.
• W2949062918 created "2019-06-27" @default.
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• W2949062918 creator A5072788154 @default.
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• W2949062918 date "2011-09-29" @default.
• W2949062918 modified "2023-09-27" @default.
• W2949062918 title "Partial theta functions and mock modular forms as q-hypergeometric series" @default.
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• W2949062918 hasPublicationYear "2011" @default.
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