Browsing by Keywords "Modular equations"
Now showing items 1-3 of 3
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Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
(Elsevier, 2012)In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. With one exception all of Ramanujan's identities were proved. In this paper, ... -
New identities for 7-cores with prescribed BG-rank
(Elsevier BV * North-Holland, 2008)Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [A. Berkovich, F.G. Garvan, On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo 5 and generalizations, ... -
On the representations of integers by the sextenary quadratic form x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2 and 7-cores
(Academic Press, 2009)In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2. We establish the following intriguing inequalities2 ω (n + 2) ≥ a7 (n) ≥ ...
