Timeline for Number-theoretic congruences with geometry and topology?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2022 at 10:36 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Feb 4, 2022 at 8:57 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Feb 4, 2022 at 4:02 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
fixed arxiv front-end links (one of them only tentative)
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| Jun 14, 2010 at 16:17 | answer | added | Mark Behrens | timeline score: 13 | |
| Jun 14, 2010 at 15:49 | answer | added | S. Carnahan♦ | timeline score: 1 | |
| Jun 14, 2010 at 15:48 | answer | added | Antun Milas | timeline score: 3 | |
| Jun 14, 2010 at 13:54 | history | edited | john mangual | CC BY-SA 2.5 |
simplification
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| Jun 14, 2010 at 8:53 | comment | added | Wadim Zudilin | Sir John, I am really lost in attempts to understand your question. I would suggest you to expand it by giving an explicit example of what you expect "in live". I have some experience with both $q$-series and congruences, but your question (its statement) puzzles me too much. | |
| Jun 14, 2010 at 8:05 | comment | added | Victor Protsak | I am not sure what this question is getting at. What is a "geometric method" and what is a "physical method" of proving an identity or a congruence? Some congruences can be obtained from identities between $q$-series. Are you asking if any such proof has a "physical" meaning? | |
| Jun 14, 2010 at 5:06 | comment | added | john mangual | No sir, this is not what I am asking for. I'm saying there are geometric interpretations of q-series identities. Often one will take a sequence of spaces and find the generating function of an invariant. Or one can take a single space and an infinite family of invariants. Mostly likely, I'm asking for examples of congruences between integer-valued invariants of manifolds and whether they can be used to prove congruences on the coefficients of q-series. For example if p(n) = the number of partitions of n, then p(5k+4) is 0 mod 5. | |
| Jun 14, 2010 at 3:46 | comment | added | Wadim Zudilin | John, why do you call the identities "congruences" (the term usually means a different thing)? If I understand your question correctly, you ask for combinatorial interpretation of $q$-series identities, restricting combinatorial objects to be physical or geometric invariants. Of course, there should be some, but as the generating series technique is more productive, the identities are probably first proven using it rather than a combinatorial argument. | |
| Jun 14, 2010 at 3:33 | history | asked | john mangual | CC BY-SA 2.5 |