Timeline for What is the relationship between modular forms and the Rogers-Ramanujan identities?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| May 18, 2013 at 7:02 | vote | accept | Vladimir Sotirov | ||
| Jun 23, 2010 at 12:05 | comment | added | Wadim Zudilin | @Vladimir: Your additional questions are hard and, in a certain sense, not well posed. For example, there are quite different opinions of whether the relationship of RRs with the modular world is coincidental. My own philosophy is that modular forms are a natural source of many sophisticated identities, as modular forms are a unique object: they satisfy two different types of functional equations. I would really suggest you to answer your items 1-3 yourself after browsing the suggested references. | |
| Jun 23, 2010 at 11:54 | comment | added | Wadim Zudilin | @Robin: Yes, you are right, in the classical RR identities and the majority of generalisations, the right-hand sides are obviously modular as products of Dedekind's etas. However, more general RR identities (e.g., ones which appear in the preprint citedd in my response) the right-hand sides are different sums for which one can still show the modularity as they are character sums for certain Virasoro algebras (but this is very sophisticated!). For the left-hand sides there is no clear way to recognise the modularity; I would guess this is related to troubles with bijective proofs... | |
| Jun 23, 2010 at 9:27 | comment | added | Robin Chapman | It's fairly straightforward that the right sides of these formulas are modular forms (see the definition of Siegel forms in the last chapter of Lang's Introduction to Modular Forms). Alas, I know no direct way of showing that the left sides are modular forms, short of proving the RR identities. I would appreciate any references to such a proof. | |
| Jun 23, 2010 at 9:01 | history | edited | Charles Matthews | CC BY-SA 2.5 |
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| Jun 23, 2010 at 7:47 | history | edited | Robin Chapman | CC BY-SA 2.5 |
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| Jun 23, 2010 at 1:30 | answer | added | Wadim Zudilin | timeline score: 3 | |
| Jun 23, 2010 at 0:11 | answer | added | SandeepJ | timeline score: 3 | |
| Jun 22, 2010 at 18:13 | answer | added | Will Jagy | timeline score: 1 | |
| Jun 22, 2010 at 16:51 | history | asked | Vladimir Sotirov | CC BY-SA 2.5 |