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- W2140147812 abstract "Ramanujan in his deathbed letter to GH Hardy concerned the asymptotic properties of modular forms and mock theta functions. For the mock theta function f(q), he claimed that as q approaches an even order 2k root of unity ζ, lim q → ζ ( f ( q ) − ( − 1 ) k ( 1 − q ) ( 1 − q 3 ) ( 1 − q 5 ) ⋯ ( 1 − 2 q + 2 q 4 − ⋯ ) ) =O(1), where (1−q)(1− q 3 )(1− q 5 )⋯(1−2q+2 q 4 −⋯)= ∏ n = 1 ∞ 1 − q n ( 1 + q n ) 2 . Recently, Folsom, Ono and Rhoades have proved two closed formulas for the implied constant and formulated an open problem which is related to their two theorems. In this note, we give a new proof on the problem of the two theorems by using some results about the generating functions of convex compositions given by GE Andrews and Appell-Lerch sums.MSC:11F37, 11F03, 11F99." @default.
- W2140147812 created "2016-06-24" @default.
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- W2140147812 date "2014-07-23" @default.
- W2140147812 modified "2023-09-24" @default.
- W2140147812 title "Note on the problem of Ramanujan’s radial limits" @default.
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- W2140147812 doi "https://doi.org/10.1186/1687-1847-2014-191" @default.
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