到凝乳 发表于 2025-3-21 16:46:54

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LIMIT 发表于 2025-3-21 23:21:16

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ACME 发表于 2025-3-22 02:03:01

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可耕种 发表于 2025-3-22 04:48:20

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我正派 发表于 2025-3-22 11:32:59

Ranks and Cranks, Part III,in prime importance. In this chapter, we examine ten tables of congruences satisfied by the coefficients of the generating function for cranks. In contrast to the well-known congruences satisfied by the partition function .(.), each of these tables has only a finite set of values, which Ramanujan re

剥皮 发表于 2025-3-22 16:36:16

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MEET 发表于 2025-3-22 17:13:24

Theorems about the Partition Function on Pages 189 and 182,) and .(7.+5)≡0 (mod 7). One of Ramanujan’s proofs hinges upon the beautiful identity . which is given on page 189. We provide a more detailed rendition of the proof given by Ramanujan, as well as a similarly beautiful identity yielding the congruence .(7.+5)≡0 (mod 7). On both pages, Ramanujan exam

Friction 发表于 2025-3-23 01:09:29

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Cholagogue 发表于 2025-3-23 03:54:58

Highly Composite Numbers,teger .<., it happens that .(.)<.(.), where .(.) is the number of divisors of .. In the notes of Ramanujan’s ., the editors relate, “The paper, long as it is, is not complete.” Fortunately, the large remaining portion of the paper was not discarded. It was first set into print by Jean-Louis Nicolas

medium 发表于 2025-3-23 08:37:31

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查看完整版本: Titlebook: Ramanujan‘s Lost Notebook; Part III George E. Andrews,Bruce C. Berndt Book 2012 Springer Science+Business Media New York 2012 Ramanujan tau