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Search: MSC category 11F27 ( Theta series; Weil representation; theta correspondences )

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1. CMB 2009 (vol 52 pp. 481)

Alaca, Ay\c{s}e; Alaca, \c{S}aban; Williams, Kenneth S.
 Some Infinite Products of Ramanujan Type In his lost'' notebook, Ramanujan stated two results, which are equivalent to the identities $\prod_{n=1}^{\infty} \frac{(1-q^n)^5}{(1-q^{5n})} =1-5\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{d} d \Big) q^n$ and $q\prod_{n=1}^{\infty} \frac{(1-q^{5n})^5}{(1-q^{n})} =\sum_{n=1}^{\infty}\Big( \sum_{d \mid n} \qu{5}{n/d} d \Big) q^n.$ We give several more identities of this type. Keywords:Power series expansions of certain infinite productsCategories:11E25, 11F11, 11F27, 30B10

2. CMB 2002 (vol 45 pp. 257)

Lee, Min Ho
 Modular Forms Associated to Theta Functions We use the theory of Jacobi-like forms to construct modular forms for a congruence subgroup of $\SL(2,\mathbb{R})$ which can be expressed as linear combinations of products of certain theta functions. Categories:11F11, 11F27, 33D10