کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665640 1633824 2014 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the dual nature of partial theta functions and Appell–Lerch sums
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On the dual nature of partial theta functions and Appell–Lerch sums
چکیده انگلیسی

In recent work, Hickerson and the author demonstrated that it is useful to think of Appell–Lerch sums as partial theta functions. This notion can be used to relate identities involving partial theta functions with identities involving Appell–Lerch sums. In this sense, Appell–Lerch sums and partial theta functions appear to be dual to each other. This duality theory is not unlike that found by Andrews between various sets of identities of Rogers–Ramanujan type with respect to Baxter's solution to the hard hexagon model of statistical mechanics. As an application we construct bilateral q-series with mixed mock modular behaviour. In subsequent work we see that our bilateral series are well-suited for computing radial limits of Ramanujan's mock theta functions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 264, 20 October 2014, Pages 236–260
نویسندگان
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