Timeline for Modular forms and "too many symmetries"
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 19, 2014 at 3:05 | comment | added | Timothy Chow | I think Mazur's perspective is that (1) the functional equation defining modular forms is something we want to hold because it has so many miraculous consequences, and (2) it is not immediately clear from the definition that such miraculous functions exist. I don't think that "so many internal symmetries" should be taken literally as a statement about cardinality. It's a statement about how the symmetries are deep. E.g., the first time you see the Rogers-Ramanujan identities, you might think it's just a formal triviality. But in fact a tremendous amount of symmetry lurks beneath the surface. | |
| Dec 18, 2014 at 20:37 | history | edited | Gjergji Zaimi |
Added an arxiv tag
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| Dec 18, 2014 at 10:26 | vote | accept | BrettW | ||
| Dec 17, 2014 at 22:51 | answer | added | Gjergji Zaimi | timeline score: 16 | |
| Dec 17, 2014 at 22:30 | comment | added | BrettW | Yes that frames it a little better. I may have been hung up thinking that Mazur meant "for a particular modular form, there are many symmetries", rather than that as well all the algebraic structures on top of modular forms in general. | |
| Dec 17, 2014 at 22:23 | comment | added | André Henriques | I'm not sure what you're asking... Maybe a better question would be to ask for a list of all the algebraic structure that is present in modular forms. "Symmetries" are only part of the total algebraic structure. For example, modular forms for a given subgroup of $SL(2,\mathbb Z)$ form a ring. But there's also Hecke operators on modular forms and I'm not sure how all these operations play together. | |
| Dec 17, 2014 at 22:17 | review | First posts | |||
| Dec 17, 2014 at 22:29 | |||||
| Dec 17, 2014 at 22:15 | history | asked | BrettW | CC BY-SA 3.0 |