Note on the problem of Ramanujan’s radial limits

@article{Chen2014NoteOT,
  title={Note on the problem of Ramanujan’s radial limits},
  author={Bin Chen and Haigang Zhou},
  journal={Advances in Difference Equations},
  year={2014},
  volume={2014},
  pages={1-11}
}
AbstractRamanujan 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, limq→ζ(f(q)−(−1)k(1−q)(1−q3)(1−q5)⋯(1−2q+2q4−⋯))=O(1), where (1−q)(1−q3)(1−q5)⋯(1−2q+2q4−⋯)=∏n=1∞1−qn(1+qn)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… 
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Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q
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Abstract Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$
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which were defined by Ramanujan and Watson decades ago. In his last letter to Hardy dated January 1920 (see pages 127-131 of [27]), Ramanujan lists 17 such functions, and he gives 2 more in his “Lost
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TLDR
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In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular
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The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper we establish for the orthogonal group O(p,2) an adjointness result
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In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews
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Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$ , where $\left| q \right|<1$ . He called them mock theta functions, because as $q$ radially approaches any
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